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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27000
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4150
 p-value of test no 16                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 17                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7051
 p-value of test no 21                 :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.16
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.37
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.28
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.94
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.68
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.66
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.54
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.28
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.81
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.95
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.51
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.80
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.76
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.19
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.63
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908174
   j =  2                              :            45907
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908683
   j =  2                              :            45651
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.71
 p-value of test no 117                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.60
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.18
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.52
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.96
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.11
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.25
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.54
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.93
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.69
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.04
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.85
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.25
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.24
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.03
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.79
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.14
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.96
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.81
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.68
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.22
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.44
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.39
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.67
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.86
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.21
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.00
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.19
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.16
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.74
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.49
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.34
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.03
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.78
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.19
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.04
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.13
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.45
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.86
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.27
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.08
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.83
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.69
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.31
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.46
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.16
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.51
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.22
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.43
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.94
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.85
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.28
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.18
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000145264
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.27
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999966083
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:06.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183271433.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27001
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.40
 p-value of test no 28                 :  5.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     657
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.72
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.52
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.34
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.93
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.32
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.03
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.09
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.65
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.48
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.39
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.27
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.30
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.59
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45390
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869390
   j =  1                              :        399909224
   j =  2                              :            45382
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907951
   j =  2                              :            46020
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.12
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.36
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.95
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.85
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.70
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.08
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.81
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.59
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.69
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.32
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.43
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.88
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.23
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.09
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.78
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.97
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.29
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.11
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.16
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.40
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.98
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.24
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.96
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.51
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.12
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.23
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.99
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.91
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.14
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.33
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.93
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.33
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.25
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.77
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.14
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.18
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.63
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.29
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.41
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.68
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.07
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.71
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.78
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.78
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.99
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.52
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.29
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.36
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.39
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.67
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.02
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4293.91
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.17
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.33
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.63
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999922784
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.16
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999912860
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.048
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:21.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184483849.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27002
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 9                  :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5251
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    3.33
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.34
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.04
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.74
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.77
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  178.65
 p-value of test no 54                 :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.31
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.91
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.99
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.71
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.70
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.71
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.59
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.54
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907856
   j =  2                              :            46066
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45522
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869522
   j =  1                              :        399908966
   j =  2                              :            45502
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.06
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.02
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.19
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.80
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.47
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.92
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.83
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.28
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.03
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.04
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.45
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17142.71
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.88
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.81
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.83
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.77
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.67
 p-value of test no 155                :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.78
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.71
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.79
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.49
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.73
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.58
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.14
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.37
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.24
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.09
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.14
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.52
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.07
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.07
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.21
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.13
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.64
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.16
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.32
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.54
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.16
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.88
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 204                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 206                :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.66
 p-value of test no 207                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.46
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.64
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.04
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4695.82
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.88
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.55
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.56
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.82
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.56
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000051058
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.68
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000044764
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:04.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185401353.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27003
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4142
 p-value of test no 14                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.85
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.71
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.47
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.34
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.30
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.39
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.76
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.29
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.94
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.24
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.66
 p-value of test no 59                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.72
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.06
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.51
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.64
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45548
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908906
   j =  2                              :            45544
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908390
   j =  2                              :            45802
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 108                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.68
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.37
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.65
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.02
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.94
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.02
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.61
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.45
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.35
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.39
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.66
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.50
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.65
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.72
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.58
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.13
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.71
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.34
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.78
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.88
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.53
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.74
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.64
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.58
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.30
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.15
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.73
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.39
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.59
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.52
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.85
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.04
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.61
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.29
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.40
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.29
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.28
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.75
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.24
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.43
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.36
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.26
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 186                :    0.9922
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.09
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.81
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.86
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.57
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.55
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.45
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.85
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.53
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.68
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.45
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.45
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.65
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.78
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000027448
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.58
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000066352
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.023
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 245                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 247                :  8.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.80
 p-value of test no 248                :  2.5e-3
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:43.42
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186351625.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27004
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     524
 p-value of test no 31                 :    0.9992    *****
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.37
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.25
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.31
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.68
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.87
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.17
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.86
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.72
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.45
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.34
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.11
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.54
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.43
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.13
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.96
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46493
 p-value of test no 70                 :  2.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870493
   j =  1                              :        399907016
   j =  2                              :            46489
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908720
   j =  2                              :            45637
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 76                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.92
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.78
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.66
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.33
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   10.81
 p-value of test no 123                : 1 -  8.0e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.25
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.38
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.93
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.32
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.90
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.97
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.58
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.69
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.85
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.19
 p-value of test no 147                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.83
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.16
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.69
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.82
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.22
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.20
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.82
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.39
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.44
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.71
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.44
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.21
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.13
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.85
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.38
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.55
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.96
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.99
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.62
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.08
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.29
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.72
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.66
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.88
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.69
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.06
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.02
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.63
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.72
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 219                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5105.93
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5141.81
 p-value of test no 226                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.15
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.33
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.08
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.52
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.24
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000061639
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.22
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000066700
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:31.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        0.9992 
  63  WeightDistrib, r = 10          1 -  8.0e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187301897.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27005
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.28
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     121
 p-value of test no 43                 :    0.9916
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    4.89
 p-value of test no 45                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.64
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.74
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.12
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.60
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.21
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.61
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.88
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.65
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.27
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.21
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.92
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907707
   j =  2                              :            46139
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 116                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.13
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.23
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.02
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.22
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.98
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.66
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.73
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.01
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.86
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.73
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.99
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.89
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.31
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.40
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.93
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.86
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.64
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.76
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.51
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.16
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.86
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.08
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.25
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.32
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.89
 p-value of test no 161                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.04
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.38
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.06
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.49
 p-value of test no 165                :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.81
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.76
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.39
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.76
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.34
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.45
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.33
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.07
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.62
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.89
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.88
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.10
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 205                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.73
 p-value of test no 207                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.90
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.91
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.63
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.14
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.42
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.23
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.86
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.16
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.51
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000024982
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.92
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000118174
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:55.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188219401.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27006
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 7                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 12                 :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5592
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7099
 p-value of test no 19                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.10
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.61
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.10
 p-value of test no 53                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.15
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.47
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.01
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.11
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.67
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.34
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.90
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5208.97
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399908000
   j =  2                              :            45988
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908655
   j =  2                              :            45665
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -3.74e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.21
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.30
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.74
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.82
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.62
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.91
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.46
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.97
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.94
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
 p-value of test no 143                :    0.9951
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17076.30
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.72
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.10
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.57
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.97
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.91
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.32
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.08
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.73
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.32
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.83
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.08
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.19
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.48
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.53
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.50
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.09
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.98
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.05
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.50
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.67
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.38
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.23
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.56
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.12
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.68
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.57
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.03
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 180                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    5.65
 p-value of test no 182                :  1.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.10
 p-value of test no 183                :    0.9990    *****
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.95
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.07
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.84
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.29
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.70
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.24
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.08
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.37
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.46
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.84
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.74
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.39
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999888743
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.69
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999818924
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 245                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:42.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  82  LempelZiv, r = 0                0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189399049.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27007
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.62
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.65
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.57
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.85
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.43
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.11
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.84
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.30
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.06
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.47
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.01
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5254.16
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45483
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869483
   j =  1                              :        399909042
   j =  2                              :            45467
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908766
   j =  2                              :            45611
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.39
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.91
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.27
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.76
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.54
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.36
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.89
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.67
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.61
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17196.88
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.37
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.72
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.83
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.33
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.74
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.20
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.62
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.92
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.39
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.53
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.89
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.53
 p-value of test no 162                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.95
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.19
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.02
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.33
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.13
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.03
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.75
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.55
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.16
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.85
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.00
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.29
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.01
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.51
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.64
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.47
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.92
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.63
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.47
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.94
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.87
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.43
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.55
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11535.08
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.76
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.99
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999880694
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.05
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999941003
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:07.44
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190611465.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27008
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.20
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.45
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.24
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.03
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.57
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.63
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.34
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.30
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.78
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.87
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.36
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.30
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.91
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4872.24
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908128
   j =  2                              :            45930
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.73
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.61
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.09
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.00
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.87
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.54
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.83
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.32
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-3
 p-value of test no 139                :    0.9987
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.45
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.43
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.25
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.58
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.26
 p-value of test no 151                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.05
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.48
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.26
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.08
 p-value of test no 156                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.32
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.54
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.84
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.99
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.65
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.66
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.39
 p-value of test no 164                :    0.9974
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.81
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.19
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.25
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.11
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.89
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.01
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.50
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.85
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.24
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.17
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.79
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.55
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.70
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9724.23
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.81
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.68
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.66
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.74
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.29
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.64
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12034.20
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.92
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000033040
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.21
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999906224
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:03.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191528969.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27009
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.02
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.72
 p-value of test no 35                 :  4.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.80
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.83
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.64
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.25
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.14
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.56
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.68
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.50
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.21
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.58
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.83
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.44
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.02
 p-value of test no 66                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.02
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.06
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46182
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870182
   j =  1                              :        399907641
   j =  2                              :            46172
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908516
   j =  2                              :            45739
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-6
 p-value of test no 113                :    0.9977
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.45
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.68
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.34
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.99
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.57
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.57
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.94
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.29
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.95
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.27
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.06
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.19
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.03
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.58
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.19
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.63
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.95
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.03
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.53
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.44
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.14
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.38
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.64
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.34
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.86
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.85
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.42
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.06
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.96
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.14
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.57
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.10
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.45
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.22
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.25
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.95
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.60
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.10
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.01
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.48
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.54
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.62
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.93
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.54
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.49
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.25
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.70
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4698.61
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.48
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.05
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.15
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.43
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.80
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999842384
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.11
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000034147
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
 p-value of test no 250                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:09.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192643081.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27010
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.00
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.52
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.88
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.88
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.31
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.33
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.80
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6887.07
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.01
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.17
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.70
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4871.54
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908458
   j =  2                              :            45759
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46283
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870283
   j =  1                              :        399907436
   j =  2                              :            46279
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9947
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.07
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.17
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.89
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.75
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.60
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.69
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.63
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.63
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.99
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.53
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.80
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.39
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.02
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.89
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.07
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.08
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.67
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.31
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.55
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.83
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.08
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.27
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.88
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.07
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.13
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.09
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.03
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.20
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.47
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.52
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.15
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.60
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.76
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.67
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.46
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.77
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.02
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.18
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    2.74
 p-value of test no 184                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.97
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.24
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.89
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.35
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.89
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.73
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.86
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.12
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.47
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.55
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.12
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.70
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999840221
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.31
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000089983
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:26.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193626121.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27011
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5576
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    2.70
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.65
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.88
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.22
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.34
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.74
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.40
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.21
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  509.71
 p-value of test no 55                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.43
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.62
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.60
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.29
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.20
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.70
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.09
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908072
   j =  2                              :            45958
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908369
   j =  2                              :            45811
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 81                 :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9900
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.25
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.87
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.06
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.61
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.71
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.03
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.05
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.76
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.21
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17273.86
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.97
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.74
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.15
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.68
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.60
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.48
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.91
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.49
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.13
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.79
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.76
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.92
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.33
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.81
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.73
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.93
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.29
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.60
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.52
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.44
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.34
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.67
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.48
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.55
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.55
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.66
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.47
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.84
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.74
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.85
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.30
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.08
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.78
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.19
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.68
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.02
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.54
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999949709
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.71
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000054349
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:16.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194773001.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27012
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 6                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     972
 p-value of test no 25                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.82
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    4.33
 p-value of test no 39                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    3.76
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.15
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.22
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.97
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.71
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.67
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.96
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.88
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.09
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.68
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.90
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.21
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.38
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.50
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908120
   j =  2                              :            45934
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908224
   j =  2                              :            45882
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 73                 :  4.7e-4    *****
 
 Anderson-Darling statistic = A2       :    4.71
 p-value of test no 74                 :  4.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.8e-3
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.53
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.49
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.34
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.71
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.77
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.84
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.22
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.62
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.32
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.61
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.45
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.95
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.22
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.94
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.12
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.77
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.97
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.34
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.67
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.98
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.01
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.19
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.40
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.79
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.65
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.92
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.87
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.29
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.81
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.60
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.15
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.87
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.95
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.43
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.57
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.65
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.91
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.29
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.33
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.56
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.60
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.20
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.81
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.78
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.83
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.45
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.38
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.01
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.40
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.76
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.32
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12117.56
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.20
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.10
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999993053
 
 Normal statistic for number of bits   :  -0.055
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.55
 p-value of test no 233                :    0.9937
 
 
 -----------------------------------------------
 Total number of bits:  7999999932
 
 Normal statistic for number of bits   : -5.38e-4
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:54.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195690505.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27013
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 8                  :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.89
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.69
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.52
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.33
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.47
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.86
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.83
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.08
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.84
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.34
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.34
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.61
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.85
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.69
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.22
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.08
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908182
   j =  2                              :            45906
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908189
   j =  2                              :            45904
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.71
 p-value of test no 115                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.13
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.91
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.74
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.93
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.13
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.51
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.03
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.20
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.58
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.71
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.24
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.12
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.71
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.05
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.05
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.45
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.04
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.95
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.78
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.12
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.80
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.14
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.15
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.76
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.41
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.03
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.36
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  289.15
 p-value of test no 166                : 1 -  9.6e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.43
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.77
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.55
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.09
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.27
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.23
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.61
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.30
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.78
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.34
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.62
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.31
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.48
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.68
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.76
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.34
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-4
 p-value of test no 219                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.59
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.44
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.02
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.47
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.46
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.92
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.45
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999936359
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.79
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999959339
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:04.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 H (L=10000, r=0)   1 -  9.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196968457.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27014
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.23
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.85
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.13
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.25
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.89
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.10
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.02
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.06
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.76
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.27
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.13
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.01
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.00
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.90
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.69
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908533
   j =  2                              :            45726
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45364
 p-value of test no 71                 :    0.9920
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869364
   j =  1                              :        399909273
   j =  2                              :            45362
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-4
 p-value of test no 110                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 111                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.66
 p-value of test no 117                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.44
 p-value of test no 118                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.30
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.01
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.46
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.28
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.80
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.65
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.16
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.66
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.82
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.65
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.93
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.23
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.60
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.79
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.05
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.35
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.62
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.05
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.38
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.09
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.46
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.61
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.05
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.21
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.35
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.75
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.38
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.85
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.60
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.90
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.42
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.16
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.98
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.71
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.35
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.69
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.30
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.49
 p-value of test no 176                :    0.9910
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.30
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.01
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.34
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.13
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.83
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.82
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.43
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.93
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.04
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.15
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.18
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.46
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000010267
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.66
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999998759
 
 Normal statistic for number of bits   : -9.81e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:59.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197984265.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27015
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9974
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.64
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.47
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.09
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.13
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.42
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.32
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.93
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.25
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.94
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.01
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.96
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.29
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.54
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.61
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.62
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.77
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908162
   j =  2                              :            45916
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908272
   j =  2                              :            45858
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.80
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.17
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.96
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.21
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.18
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.79
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.97
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.14
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.73
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.04
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.93
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.99
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.45
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.76
 p-value of test no 151                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.19
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.72
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.76
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.99
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.86
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.14
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.28
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.07
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.50
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.82
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.22
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.70
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.09
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.37
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.48
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.22
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.89
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.68
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.55
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.36
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.11
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.95
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.66
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.79
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.13
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.23
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.76
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.24
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.90
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.75
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12096.68
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.45
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.99
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999960623
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.80
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999994094
 
 Normal statistic for number of bits   :  -0.047
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:09.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198934537.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27016
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.08
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.81
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.37
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.24
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.45
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.13
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.22
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.56
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.87
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.19
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.71
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.69
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.24
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.26
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5343.91
 p-value of test no 68                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908214
   j =  2                              :            45890
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 84                 :    0.9902
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.28
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.64
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.11
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.58
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.56
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.63
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.67
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.55
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.72
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.24
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.57
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.00
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   65.28
 p-value of test no 146                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.68
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.55
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.53
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.61
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.87
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.27
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.93
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.04
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.17
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.61
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.12
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.15
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.33
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.47
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.33
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.95
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.40
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.32
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.46
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.02
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.66
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.59
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.84
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.52
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.68
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.80
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.48
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.49
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.64
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.00
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.57
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.58
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.81
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.58
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.37
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.27
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.36
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.97
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4710.57
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4305.41
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.53
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.36
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.22
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.10
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000055237
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.37
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999967553
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:34.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199917577.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27017
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.27
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.81
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.16
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.20
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.34
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.18
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.62
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.90
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.52
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.99
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.62
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.42
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45591
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869591
   j =  1                              :        399908820
   j =  2                              :            45587
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908208
   j =  2                              :            45890
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.28
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.01
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.68
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.16
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.97
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.75
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.85
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.75
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.10
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.29
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17374.10
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.73
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.80
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.06
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.99
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.10
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.92
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.69
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.41
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.68
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.01
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.16
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.47
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.84
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.64
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.25
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.97
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.15
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.60
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  117.75
 p-value of test no 165                :  9.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.92
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.81
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.33
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.05
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.66
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.15
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.27
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4807.39
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.49
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.54
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.04
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.30
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.62
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.15
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.37
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.29
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.22
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -4.74
 p-value of test no 217                : 1 -  1.1e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.35
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.84
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3915.64
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.20
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12087.10
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.76
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.51
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000092647
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.70
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000114742
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:18.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    9.2e-4
  93  HammingCorr, L = 300           1 -  1.1e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200867849.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27018
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 12                 :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.62
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.72
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.17
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.43
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.35
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.72
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.36
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.70
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6891.08
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.09
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.09
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.76
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.66
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.02
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45366
 p-value of test no 70                 :    0.9918
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869366
   j =  1                              :        399909272
   j =  2                              :            45358
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908331
   j =  2                              :            45824
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 92                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.27
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.66
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.55
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.85
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.88
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.64
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.29
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.27
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17182.14
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.01
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.32
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.41
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.81
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.80
 p-value of test no 150                :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.75
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.44
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.82
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.95
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.11
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.80
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.12
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.36
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.72
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.29
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.28
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.44
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.26
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.01
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.40
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.57
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.40
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.27
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.63
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.99
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.90
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.48
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.49
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.19
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.87
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.40
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.91
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.11
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.15
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.63
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.85
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.50
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.92
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.24
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.01
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.90
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.94
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999946892
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.22
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999945002
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:14.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft AD, t = 24               0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202014729.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27019
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 10                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4552
 p-value of test no 17                 :  6.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.12
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.53
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.78
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.74
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.95
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.60
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.85
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.28
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.21
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.19
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.97
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.13
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5248.18
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908583
   j =  2                              :            45707
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908202
   j =  2                              :            45890
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 98                 :    0.9923
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.18
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.28
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.58
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.59
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.72
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-4
 p-value of test no 126                :    0.9990    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.92
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.19
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.34
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17698.02
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.78
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.67
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.22
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.51
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.91
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.08
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.74
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.55
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.61
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.97
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.58
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.70
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.39
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.24
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.11
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.15
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.32
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.39
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.68
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.18
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.62
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.70
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.46
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.94
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.29
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.43
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.81
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.34
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.83
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 200                :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.12
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.21
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.70
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.82
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.32
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.01
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.85
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.94
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.09
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.61
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.90
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999976373
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000006697
 
 Normal statistic for number of bits   :   0.053
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:04.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203030537.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27020
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 9                  :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7082
 p-value of test no 15                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    3.26
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.12
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.58
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.24
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.32
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.45
 p-value of test no 53                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.08
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.31
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.24
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.09
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.44
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.26
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.58
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   81.86
 p-value of test no 67                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.59
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908851
   j =  2                              :            45570
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908430
   j =  2                              :            45776
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.69
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.38
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.24
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.86
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.17
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.81
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.25
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.91
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.72
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17688.83
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   67.58
 p-value of test no 146                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.94
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.18
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.32
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.07
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.71
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.67
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.81
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.73
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.29
 p-value of test no 159                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.26
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.57
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.28
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.82
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.12
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.69
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.26
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.02
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.85
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.65
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.54
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.55
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.76
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.32
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.30
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.47
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.80
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.19
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.67
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.33
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.64
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.22
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.27
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.35
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.11
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.36
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4327.99
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.96
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.27
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.60
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999974783
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.37
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999918449
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-4
 p-value of test no 235                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.70
 p-value of test no 238                :  3.5e-3
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:57.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183304202.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27021
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 4                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.44
 p-value of test no 23                 :  5.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9939
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.11
 p-value of test no 47                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.59
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.40
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.81
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.45
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.05
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.25
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.95
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.26
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.50
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.99
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.57
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.43
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4797.88
 p-value of test no 68                 :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908466
   j =  2                              :            45761
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908045
   j =  2                              :            45970
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
 p-value of test no 72                 :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.17
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.99
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.43
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.79
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.64
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.97
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.40
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17648.30
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.16
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.74
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.58
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.84
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.32
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.19
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.73
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.01
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.64
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.21
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.07
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.92
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.36
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.32
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.98
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.89
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.69
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.21
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.09
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.13
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.24
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.93
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.76
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.97
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.20
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.00
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.82
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.46
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.77
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.92
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.32
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.70
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.20
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.03
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.79
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.78
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.77
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.14
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.82
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.48
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.10
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000229330
 
 Normal statistic for number of bits   :    1.81
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.95
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000045484
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.16
 p-value of test no 244                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-4
 p-value of test no 245                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.80
 p-value of test no 248                :  2.5e-3
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:36.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184451082.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27022
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 11                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.27
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.33
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.41
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.77
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.45
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.29
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.99
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.90
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.58
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-4
 p-value of test no 58                 :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.09
 p-value of test no 61                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.75
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.07
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.95
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907659
   j =  2                              :            46169
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908119
   j =  2                              :            45939
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.85
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.80
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.31
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.43
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.39
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.60
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.33
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
 p-value of test no 131                : 1 -  6.1e-5    *****
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.63
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.26
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.40
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.68
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.30
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.17
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.42
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.38
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.04
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.45
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.90
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.26
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.49
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.58
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.63
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.42
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.05
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.92
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.26
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.35
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.11
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.26
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.46
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.31
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.50
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.23
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.09
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.49
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.47
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.82
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.89
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.34
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.60
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.53
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.57
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.27
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 209                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.98
 p-value of test no 210                :  3.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10398.95
 p-value of test no 211                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.01
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.51
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.84
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.94
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.57
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.70
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.61
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.18
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000043147
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.86
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000138724
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:09.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185303050.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27023
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.58
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.81
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.52
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.47
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.32
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.93
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.00
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.15
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.83
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.62
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.92
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.79
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.43
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.55
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908207
   j =  2                              :            45895
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
 p-value of test no 77                 :    0.9941
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.49
 p-value of test no 115                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.46
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.64
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.56
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.52
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.44
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.90
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.54
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.15
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.25
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.81
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.16
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.39
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.07
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.99
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.63
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.66
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.06
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.39
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.30
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.07
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.38
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.72
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.99
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.63
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.14
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.60
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.20
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.81
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.84
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.06
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.18
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.54
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.31
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.58
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.82
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.81
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.23
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.51
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.25
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.08
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.59
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.28
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.15
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.29
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.91
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.88
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.51
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.14
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.02
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.51
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.10
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999906869
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.50
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999973547
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.76e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:27.75
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186187786.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27024
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    3.43
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.59
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.97
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.25
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.31
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.60
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.19
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.86
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 58                 :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   55.89
 p-value of test no 61                 :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.77
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.53
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.37
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.94
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908125
   j =  2                              :            45927
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908361
   j =  2                              :            45818
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 95                 :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 105                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.50
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.58
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.87
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.70
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.17
 p-value of test no 125                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.49
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.58
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.78
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17292.73
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.23
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.76
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.76
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.12
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.09
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.58
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.40
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.74
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.95
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.67
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.31
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.17
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.92
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.53
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.68
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.29
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.65
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.87
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.23
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.80
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.29
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.94
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.57
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.40
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.98
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.92
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.44
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.21
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 209                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10290.98
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.65
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.75
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.45
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.31
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.59
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.21
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.38
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.30
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000074935
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.32
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000044254
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.029
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 248                :    0.48
 
 Sample variance                       :    2.11
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187170826.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27025
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 9                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.87
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.54
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.47
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.27
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.46
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.79
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.01
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.98
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.71
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.96
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.52
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.97
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.14
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.37
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908015
   j =  2                              :            45991
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907731
   j =  2                              :            46130
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.71
 p-value of test no 115                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.53
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.96
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.86
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.93
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.32
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.06
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.93
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.83
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.15
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.91
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17301.76
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.08
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.29
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.56
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.69
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.54
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.99
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.78
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.64
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.06
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.22
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.76
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.78
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.45
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.52
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.96
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.48
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.75
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.17
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.39
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.95
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.97
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.55
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.93
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.05
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.50
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.75
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.97
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.79
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.99
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.21
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.45
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.68
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.47
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.14
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.97
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.98
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.13
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.52
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.75
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.16
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12278.64
 p-value of test no 230                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.64
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000006970
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.79
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000093226
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:58.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188121098.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27026
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 6                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.19
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.00
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.93
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.90
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.06
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  367.45
 p-value of test no 55                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.63
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.02
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.71
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.60
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.11
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.95
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.91
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908519
   j =  2                              :            45733
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908121
   j =  2                              :            45926
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 90                 :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.86
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.80
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.86
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.20
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.87
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.57
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.093
 p-value of test no 134                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   18.25
 p-value of test no 135                :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.96
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.52
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.00
 p-value of test no 146                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.54
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.00
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.91
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.41
 p-value of test no 150                :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.68
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.11
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.29
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.19
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.88
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.21
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.35
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.72
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.81
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.15
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.11
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.05
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.23
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.18
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.61
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.72
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.58
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.21
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.03
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.89
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.73
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.18
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.52
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.37
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.79
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 195                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.48
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 200                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 202                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  263.34
 p-value of test no 203                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.45
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.49
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.99
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.64
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.97
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.75
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.70
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.28
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.35
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.63
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000111046
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.36
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000054934
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:28.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189136906.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27027
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.46
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.14
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.01
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.13
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.84
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.22
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.05
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.75
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.20
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.55
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.29
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.11
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.46
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.66
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.36
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.82
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908619
   j =  2                              :            45689
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908141
   j =  2                              :            45922
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.46
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.76
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.38
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.48
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.93
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.58
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.57
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.70
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.59
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.60
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.85
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.50
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.09
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.61
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.91
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.13
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.94
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.96
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.42
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.44
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.91
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.98
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.87
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.46
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.24
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.82
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.37
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.58
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.42
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.46
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.07
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.91
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.04
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.70
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.47
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.47
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.13
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.39
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.89
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.70
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.10
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.62
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.93
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.32
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4399.26
 p-value of test no 227                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.43
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.46
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.01
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.85
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000076507
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.58
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000046405
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:48.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190119946.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27028
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 11                 :    0.9977
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7526
 p-value of test no 18                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.85
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.13
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.25
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.77
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.74
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.35
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.66
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.58
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1348.97
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7000.20
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 58                 :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.15
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.07
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.77
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.95
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.60
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907539
   j =  2                              :            46226
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908217
   j =  2                              :            45887
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-4
 p-value of test no 79                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 81                 :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  6.4e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 100                :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.80
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.43
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.92
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.96
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.55
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.09
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.77
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.28
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.00
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17014.24
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.22
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.00
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.95
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.66
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.13
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.27
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.81
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.89
 p-value of test no 154                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.06
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.95
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.76
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.65
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.59
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.40
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.94
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.76
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.84
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.21
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.98
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.37
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.38
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.94
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.41
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.70
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.11
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.45
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.25
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.79
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.45
 p-value of test no 176                :    0.9915
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.91
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.82
 p-value of test no 179                :    0.9976
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.62
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.02
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.32
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.52
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.45
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.45
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.36
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.93
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.98
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.92
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.37
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.25
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999776108
 
 Normal statistic for number of bits   :   -1.77
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.69
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000100234
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:54.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191135754.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27029
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.74
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.76
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.47
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.93
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.94
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.56
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.00
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.08
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.09
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.82
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.92
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.83
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908670
   j =  2                              :            45662
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908687
   j =  2                              :            45655
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.55
 p-value of test no 118                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.70
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.60
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.98
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.45
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.64
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.25
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.18
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.99
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.94
 p-value of test no 134                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.02
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.64
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.38
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.02
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.57
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.34
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.74
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.94
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.50
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.29
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.63
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.20
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.96
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.49
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.46
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.86
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.83
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.38
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.65
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.39
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.82
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.61
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.83
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.71
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.79
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.50
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.78
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.83
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.36
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.69
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.76
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.30
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.67
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.57
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.82
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5082.91
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.38
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4339.51
 p-value of test no 228                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12174.50
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11599.02
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.84
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999985598
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.67
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999916544
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:24.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192118794.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27030
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 8                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.99
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.05
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.79
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.13
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.20
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.75
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.13
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.17
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6788.85
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.09
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.12
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.09
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.14
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4856.92
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908670
   j =  2                              :            45662
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908592
   j =  2                              :            45698
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 78                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.25
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.71
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.74
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.49
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.81
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.99
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.11
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.38
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.47
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.87
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   18.25
 p-value of test no 135                :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.43
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17279.54
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.85
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.84
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.82
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.60
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.79
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.30
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.36
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.32
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.65
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.27
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.50
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.09
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.88
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.94
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.28
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.26
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.11
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.92
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.48
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.80
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.15
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.02
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.38
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.12
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.06
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.08
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.11
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.48
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.48
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.37
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 206                :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.22
 p-value of test no 207                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.08
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.89
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.34
 p-value of test no 217                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.59
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.96
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.30
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.80
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.65
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.04
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.67
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999871526
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.59
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000119365
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 245                :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:58.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193232906.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27031
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.67
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.11
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.09
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.93
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.31
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.84
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.37
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.88
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.08
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.19
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.07
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.30
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.25
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5248.02
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907957
   j =  2                              :            46017
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908284
   j =  2                              :            45852
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 90                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
 p-value of test no 103                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 105                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.55
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.78
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.91
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.26
 p-value of test no 123                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.05
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.85
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.76
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.94
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.93
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.91
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.51
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.42
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.29
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.45
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.74
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.97
 p-value of test no 151                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.02
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.82
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.80
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.31
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.09
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.33
 p-value of test no 159                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.13
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.41
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.32
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.59
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.70
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.55
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.22
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.13
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.28
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.71
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.36
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.10
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.92
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.66
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.54
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.54
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.23
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    2.19
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.44
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 201                :    0.9928
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.77
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.37
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.72
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.44
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.30
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4700.81
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.63
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.37
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.05
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.77
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.29
 p-value of test no 231                :  9.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999819989
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.78
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000136027
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:42.51
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194379786.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27032
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4167
 p-value of test no 14                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     836
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.64
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.39
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.63
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.64
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.58
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.37
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.56
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.01
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.49
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.35
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.76
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.51
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.91
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45612
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869612
   j =  1                              :        399908778
   j =  2                              :            45608
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908080
   j =  2                              :            45954
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.04
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.80
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.79
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.23
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.76
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.38
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.59
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.87
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.10
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.79
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.22
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.76
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.99
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.33
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.36
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.61
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.12
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.44
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.48
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.74
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.78
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.21
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.78
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.93
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.93
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.80
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.12
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.13
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.87
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.41
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.73
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.26
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.24
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.73
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.56
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.35
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.19
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.17
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.55
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.45
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.19
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.22
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.89
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.12
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.70
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.44
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.61
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.98
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.80
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.31
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000001963
 
 Normal statistic for number of bits   :   0.016
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.30
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999880085
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.067
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.100
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:56.80
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195624970.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27033
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    3.23
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     971
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.90
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.93
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.24
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.47
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.01
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.74
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.23
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.32
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.15
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.54
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.57
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.00
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.66
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.40
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908270
   j =  2                              :            45862
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.75
 p-value of test no 115                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.21
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.65
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.91
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.00
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.80
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.03
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.74
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.52
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.92
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.33
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.09
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.58
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.33
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.45
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.02
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.60
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.19
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.75
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.58
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.09
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.81
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.88
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.97
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.92
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.14
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.70
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.09
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.30
 p-value of test no 162                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.00
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.75
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.90
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.62
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.79
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.09
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.23
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.51
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.80
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.30
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.25
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.02
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.02
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 185                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.15
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.62
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.36
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.91
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.72
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.37
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.02
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.75
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.07
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.37
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.01
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999971819
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.01
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000210640
 
 Normal statistic for number of bits   :    1.67
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:34.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196542474.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27034
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    2.49
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.48
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.35
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.15
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.93
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.93
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.38
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.09
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7269.01
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.27
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.08
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.53
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.25
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45477
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869477
   j =  1                              :        399909047
   j =  2                              :            45475
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908140
   j =  2                              :            45912
   j =  3                              :               12
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
 p-value of test no 72                 :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  9.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 93                 :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    5.22
 p-value of test no 95                 :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  6.6e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.21
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.27
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.27
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.20
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.41
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.86
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.26
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.06
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.28
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.71
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.77
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.45
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.31
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.30
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.34
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.81
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.50
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.34
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.04
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.98
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.03
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.50
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.60
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.69
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.87
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.33
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.06
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.22
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.97
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.72
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.40
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.27
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.84
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  472.52
 p-value of test no 172                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.46
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.61
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.03
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.31
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.66
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    2.19
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.64
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.55
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.42
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.68
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.25
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.09
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.45
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.12
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.32
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.90
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.57
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000086215
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.84
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999952034
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    2.28
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:06.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197722122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27035
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1497
 p-value of test no 12                 :  2.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334617
   j =  1                              :        599997006
   j =  2                              :             1497
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5593
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 20                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.95
 p-value of test no 35                 :  9.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.30
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.82
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.00
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.76
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.44
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.54
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  509.12
 p-value of test no 55                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.20
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.53
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.01
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.97
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.55
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.91
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908001
   j =  2                              :            45995
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908286
   j =  2                              :            45857
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.60
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.90
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.93
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.74
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.70
 p-value of test no 123                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.48
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.63
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.81
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.70
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.53
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17466.06
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.44
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.85
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.97
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.32
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.38
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.62
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.93
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.54
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.86
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.79
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.69
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.48
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.61
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.15
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.19
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.42
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.87
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.27
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.51
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.28
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.35
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.24
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.27
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4797.28
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.68
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.30
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.38
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.40
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.50
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.77
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.54
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.86
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.08
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.70
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.07
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.11
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.95
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999997601
 
 Normal statistic for number of bits   :  -0.019
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.83
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000162850
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:39.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198869002.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27036
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.42
 p-value of test no 41                 :  6.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.05
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.58
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.01
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.99
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.41
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.21
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.98
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.18
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.01
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.99
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.71
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.75
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4915.70
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908519
   j =  2                              :            45736
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908025
   j =  2                              :            45980
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.75
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.19
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.83
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.82
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.71
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.79
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.49
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.16
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.16
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.44
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.49
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.87
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.23
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.20
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.79
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.89
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.09
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.49
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.68
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.58
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.33
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.22
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.37
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.57
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.08
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.01
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.12
 p-value of test no 163                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.21
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.22
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.30
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.57
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.78
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.91
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.91
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.67
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.16
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.96
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.04
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.32
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.79
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.29
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.26
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.22
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.21
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.07
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.89
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 225                :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4618.46
 p-value of test no 226                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.49
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.43
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.44
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.59
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000041887
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999830036
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:01.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199819274.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27037
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    5.26
 p-value of test no 27                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.80
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.13
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.41
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.34
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.88
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.36
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.41
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1348.46
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7258.30
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.28
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.23
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.34
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5216.82
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45397
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869397
   j =  1                              :        399909209
   j =  2                              :            45391
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908519
   j =  2                              :            45730
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.80
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.08
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.77
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.52
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.76
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.85
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.63
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.03
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.65
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.43
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.14
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.42
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.61
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.65
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.60
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.20
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.75
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.54
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.55
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.52
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.16
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.31
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.14
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.49
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.04
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.46
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.14
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.23
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.43
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.67
 p-value of test no 166                :  9.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.14
 p-value of test no 167                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.13
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.00
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.22
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.94
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.21
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.33
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.45
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.43
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.62
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.57
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.86
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.85
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.47
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.35
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.86
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.76
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.58
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.32
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.55
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.80
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000107455
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.70
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000016699
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:40.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200802314.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27038
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    8.65
 p-value of test no 45                 :  6.0e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.93
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   40.55
 p-value of test no 49                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.48
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.25
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.76
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.50
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.16
 p-value of test no 55                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.28
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.45
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.81
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.32
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.64
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.82
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.70
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907841
   j =  2                              :            46075
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907991
   j =  2                              :            46003
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.00
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.68
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.41
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.02
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.92
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.34
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.19
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.77
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.64
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.39
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.13
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.68
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.06
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.22
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.06
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.36
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.91
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.50
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.58
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.82
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.06
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.05
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.42
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.15
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.09
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.87
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.76
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.46
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.23
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.14
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.01
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.55
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.31
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.62
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.88
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.53
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.12
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 185                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.99
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.89
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.67
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.81
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.17
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.73
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.60
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.01
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.26
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11542.17
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.78
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.81
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999868223
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.43
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000171142
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        6.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201818122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27039
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5273
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.17
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.54
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.64
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.84
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.26
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.07
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.54
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.53
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.50
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.04
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.50
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.24
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.33
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5259.64
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908009
   j =  2                              :            45994
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46184
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907635
   j =  2                              :            46178
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 108                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.54
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.47
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.39
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.15
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.63
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.84
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.96
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17130.48
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.87
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.27
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.79
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.73
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.79
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.51
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.77
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.30
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.24
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.75
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.07
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.71
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.41
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.89
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.46
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.75
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.88
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.31
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.45
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.08
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.95
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.27
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.52
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.18
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.15
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.21
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.75
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.85
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.49
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.15
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.86
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.80
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.36
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.66
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.58
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 219                :  2.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    5.58
 p-value of test no 221                :  1.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4584.38
 p-value of test no 222                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.78
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.28
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.48
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.47
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11503.22
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.18
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999982283
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.93
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999894884
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:00:10.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202768394.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27040
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.58
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.84
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.37
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.84
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.89
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.67
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.97
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.57
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7295.02
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.88
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.03
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.07
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.71
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908725
   j =  2                              :            45636
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907733
   j =  2                              :            46126
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.65
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.77
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.05
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.92
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.81
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.45
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.68
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.49
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.28
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17557.47
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.84
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.16
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.07
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.97
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.56
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.81
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.28
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.34
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.05
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.56
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.76
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.13
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.13
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.46
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.33
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.70
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.61
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.15
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.86
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.46
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.65
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.98
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.74
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.58
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.84
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.75
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.51
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.82
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.46
 p-value of test no 174                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.81
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.58
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.93
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.87
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.90
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.62
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5081.88
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.41
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.71
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.58
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.36
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.84
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.25
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000060589
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   89.22
 p-value of test no 233                :  1.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000223474
 
 Normal statistic for number of bits   :    1.77
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 241                :    0.9934
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:42.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183336971.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27041
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    3.70
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.52
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.53
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.24
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.79
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.88
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.79
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.17
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.24
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.20
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.57
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.29
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.98
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.27
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.00
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46225
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870225
   j =  1                              :        399907554
   j =  2                              :            46217
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908469
   j =  2                              :            45758
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.11
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.59
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.50
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.61
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.35
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.21
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.87
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.03
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.01
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17694.29
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.61
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.50
 p-value of test no 147                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.52
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.69
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.76
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.22
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.85
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.48
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.36
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.15
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.04
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.64
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.97
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.25
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.81
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.14
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.86
 p-value of test no 166                :  9.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.16
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.81
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.58
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.48
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.65
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.53
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.33
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.45
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.88
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.12
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.16
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.05
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.74
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.62
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.90
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.39
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.50
 p-value of test no 216                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.32
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.80
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.79
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.74
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.08
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.21
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.80
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999962018
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.19
 p-value of test no 233                :    0.9977
 
 
 -----------------------------------------------
 Total number of bits:  7999890453
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    3.06
 p-value of test no 239                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:30.97
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184320011.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27042
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 5                  :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 10                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5328
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.38
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.65
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.89
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.58
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.10
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.92
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.64
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.59
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.31
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.93
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.79
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.65
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.88
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46142
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870142
   j =  1                              :        399907720
   j =  2                              :            46134
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908319
   j =  2                              :            45833
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 77                 :    0.9964
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.11
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.66
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.90
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.39
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.22
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.49
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.06
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.07
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.82
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.05
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.27
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.69
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.48
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.00
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.72
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.68
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.27
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.24
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.73
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.85
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.22
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.72
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.37
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.34
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.27
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.01
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.77
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.02
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.42
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.80
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.15
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.25
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.38
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.63
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.05
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.93
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    2.10
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.67
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.36
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.54
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.87
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10218.38
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.73
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.68
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4296.51
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.38
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.75
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.26
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.35
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999971768
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.42
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000056776
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:55.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185630731.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27043
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.64
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.00
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.53
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.33
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.12
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.02
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.92
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.18
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.49
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.95
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5235.41
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907722
   j =  2                              :            46133
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908455
   j =  2                              :            45771
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.93
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.68
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.52
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.35
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.01
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.26
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.12
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.27
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 143                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    5.56
 p-value of test no 144                :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18018.52
 p-value of test no 145                :  9.0e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.38
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.27
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.46
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.21
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.77
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.07
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.63
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.07
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.81
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.84
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.97
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.11
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.39
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.54
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.13
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.87
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.90
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.88
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.00
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.07
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.28
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.08
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.42
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.21
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.24
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.05
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.81
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.60
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.12
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.41
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.96
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.69
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.00
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.24
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.66
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.46
 p-value of test no 216                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4725.41
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4673.09
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.29
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.26
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.60
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12106.22
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.37
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999831911
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.16
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999874124
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.98
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:04.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  73  GCD                             9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186810379.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27044
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.47
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.36
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.95
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.71
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.34
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.88
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.76
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.31
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.83
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.12
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.96
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.75
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.61
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.55
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908149
   j =  2                              :            45915
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46140
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907722
   j =  2                              :            46136
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.20
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.65
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.32
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.29
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.41
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.34
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.55
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.86
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.03
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.03
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.23
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.07
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.80
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.56
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.17
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.10
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.75
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.56
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.51
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.46
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.23
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.61
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.90
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.65
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.41
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.59
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.65
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.29
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.33
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.16
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.95
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.28
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.64
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.32
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.35
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.54
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.46
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.44
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.83
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9697.41
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.47
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.97
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.32
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4339.64
 p-value of test no 227                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.11
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.12
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.66
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.40
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000047935
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.04
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999812315
 
 Normal statistic for number of bits   :   -1.48
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:35.77
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187760651.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27045
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5564
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.79
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.11
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.84
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.31
 p-value of test no 51                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.59
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.71
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.38
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.54
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.33
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.98
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.86
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.88
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.67
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907984
   j =  2                              :            46005
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.61
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.32
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.71
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.31
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.13
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.78
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.20
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.80
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.30
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.35
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.78
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.30
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.90
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.37
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.27
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.75
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.05
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.71
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.56
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.95
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.57
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.04
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.92
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.43
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.13
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.95
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.91
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.39
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.56
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.08
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.98
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.26
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.82
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.52
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.91
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.49
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.23
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.95
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.04
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 183                :    0.89
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.66
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.84
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.24
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.31
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.68
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.00
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.98
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.39
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.41
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.32
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12141.21
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.32
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999969620
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.83
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000018199
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:25.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188678155.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27046
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1242
 p-value of test no 9                  :    0.9996    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334362
   j =  1                              :        599997516
   j =  2                              :             1242
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.26
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.43
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.92
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.99
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.62
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.74
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.48
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.00
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.72
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.19
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.51
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.38
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.17
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.89
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46255
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870255
   j =  1                              :        399907495
   j =  2                              :            46245
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907782
   j =  2                              :            46100
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 105                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.17
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.77
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.84
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.24
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.90
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.02
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.29
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.94
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.40
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.19
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.10
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.09
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.64
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.11
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.25
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.80
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.37
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.65
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.75
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.68
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.74
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.16
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.23
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.23
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.37
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.49
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.18
 p-value of test no 166                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.13
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.58
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.29
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.02
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.32
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.43
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.70
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.93
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.28
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.84
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.44
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.17
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.08
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.64
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.88
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 212                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9764.45
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.65
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.25
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.29
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3896.97
 p-value of test no 228                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.78
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.10
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.39
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000124777
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.64
 p-value of test no 233                :  4.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999982382
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.16
 p-value of test no 254                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:07.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9996 
  51  SampleProd, t = 16              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189595659.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27047
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    4.96
 p-value of test no 44                 :  3.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.60
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.43
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.66
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.79
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.83
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.78
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7229.66
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.05
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.96
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.88
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.29
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.87
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908476
   j =  2                              :            45759
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.97
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.15
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.66
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.86
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.65
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.39
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.80
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.33
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.42
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.92
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.16
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.14
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.70
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.18
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.79
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.56
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.80
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.13
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.83
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.68
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.30
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.37
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.08
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.69
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.60
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.57
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.76
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.20
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.69
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.01
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.48
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.89
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.13
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.72
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.25
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.75
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.60
 p-value of test no 177                :    0.9953
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.10
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.78
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.64
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.62
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9812.53
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.46
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.71
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.71
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.81
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.18
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.27
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.31
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000057955
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.29
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999995792
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:09.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190578699.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27048
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.68
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.22
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.03
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.64
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.31
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  283.12
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.18
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.72
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.80
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.66
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.51
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.87
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.88
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.01
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908116
   j =  2                              :            45936
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907850
   j =  2                              :            46066
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.05
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.67
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.08
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.28
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.91
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.39
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.37
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.89
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.94
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.09
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.20
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.33
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.55
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.86
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.25
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.88
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.11
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.73
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.95
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.63
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.64
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.10
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.90
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.54
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.33
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.27
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.04
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.75
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.66
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.05
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.61
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.90
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.60
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.25
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.68
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.69
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.40
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.38
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.61
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.22
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.37
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.55
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.04
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.37e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.89
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.13
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.79
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.77
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.73
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.48
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.52
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999994553
 
 Normal statistic for number of bits   :  -0.043
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.97
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000017092
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:16.82
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191496203.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27049
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997221
   j =  2                              :             1388
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.08
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.65
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.95
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.61
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.50
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.49
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.28
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.97
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7278.03
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.39
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-3
 p-value of test no 63                 :    0.9985
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.35
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.62
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.22
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.13
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907867
   j =  2                              :            46062
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907790
   j =  2                              :            46105
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 85                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.13
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.69
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.40
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.03
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.28
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.40
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.06
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.31
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.29
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.27
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.63
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.25
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.51
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.63
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.99
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.72
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.16
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.82
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.95
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.24
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.58
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.32
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.60
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.09
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.86
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.22
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.83
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.20
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.51
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.37
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.21
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.94
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.75
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.49
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5179.37
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.29
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.56
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.76
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.42
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.08
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.63
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.10
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.60
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.14
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.95
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.94
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.21
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.12
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.72
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.23
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999957413
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.77
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000113164
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:38.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192479243.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27050
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5532
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.85
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.94
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.58
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.38
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.26
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.46
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.16
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.61
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.20
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.26
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.12
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.50
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.35
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.14
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908184
   j =  2                              :            45902
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908807
   j =  2                              :            45589
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 86                 :    0.9900
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.12
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.34
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.55
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.48
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.32
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.90
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.93
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.60
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.99
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17577.62
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.81
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.17
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.55
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.69
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.74
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.23
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.25
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.67
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.85
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.09
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.25
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.06
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.52
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.22
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.36
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.93
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.30
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.22
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.82
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5201.69
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.04
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.67
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.18
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.19
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.55
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.95
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.38
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.59
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.77
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.70
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.60
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.89
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4274.78
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.51
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.18
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.11
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000055096
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.36
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000080521
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:51.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193789963.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27051
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4156
 p-value of test no 14                 :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7068
 p-value of test no 18                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.50
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.27
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.83
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.41
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.20
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.78
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.18
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.05
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.47
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.86
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.37
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.32
 p-value of test no 66                 :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.29
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.73
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908399
   j =  2                              :            45796
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46194
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870194
   j =  1                              :        399907616
   j =  2                              :            46186
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.86
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.61
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.78
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.99
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.35
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.49
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.55
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.03
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.52
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17687.93
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.85
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.92
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.63
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.52
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.61
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.61
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.29
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.80
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.56
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.63
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.42
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.69
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.51
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.74
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.56
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.76
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.84
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.51
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4819.96
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.63
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.93
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.91
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.29
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.85
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.74
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.74
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.29
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.94
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.64
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.53
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.34
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.46
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.65
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.53
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.40
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.28
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.96
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000016252
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.57
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999926690
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:31.82
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194838539.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27052
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 5                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.46
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.93
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.46
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.26
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.91
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.06
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.48
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.36
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.73
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.37
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.95
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.49
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907669
   j =  2                              :            46164
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908212
   j =  2                              :            45894
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.28
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.37
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.48
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.48
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.28
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.66
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.02
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.49
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.57
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.68
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.25
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.02
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.10
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.79
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.10
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.75
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.44
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.56
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.30
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.86
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.40
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.87
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.62
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.78
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.74
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.35
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.49
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.55
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.25
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.56
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.94
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.02
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.75
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.96
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.29
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.50
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.21
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.14
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.96
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.87
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.63
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.35
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.69
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.39
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.99
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.01
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.75
 p-value of test no 231                :  4.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000140188
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.85
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999891956
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    2.03
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:57.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195821579.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27053
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 12                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.52
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.80
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.60
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.64
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.99
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.25
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.12
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.18
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.92
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.43
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.81
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.78
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.88
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.49
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908324
   j =  2                              :            45829
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46437
 p-value of test no 71                 :  4.7e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870437
   j =  1                              :        399907128
   j =  2                              :            46433
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.36
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.96
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.09
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.40
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.31
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.42
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.37
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.61
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.37
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17550.01
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.06
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.58
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.55
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.89
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.90
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.99
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.55
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.28
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.86
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.79
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.34
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.50
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.94
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.97
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.77
 p-value of test no 164                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.88
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.62
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.48
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.96
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.01
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.11
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.41
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.98
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.16
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.42
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.83
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.86
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.35
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.18
 p-value of test no 184                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.37
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.98
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.56
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.17
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.94
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3865.11
 p-value of test no 227                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.59
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.97
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12069.72
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000017443
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.07
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999949352
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 242                :  4.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.89
 p-value of test no 243                :  1.9e-3
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:32.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196804619.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27054
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.02
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.07
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.60
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.44
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.35
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.12
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.99
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.60
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.68
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.72
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.84
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.70
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.01
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.29
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.24
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908136
   j =  2                              :            45929
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 91                 :    0.9921
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.44
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.12
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.18
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.07
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.96
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.98
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.68
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.25
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17623.66
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.40
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.44
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.19
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.33
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.00
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.66
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.86
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.96
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.79
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.07
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.02
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.47
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.97
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.44
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.56
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.97
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.60
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.57
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4801.91
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.67
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.09
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.32
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.35
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.27
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.45
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.72
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.86
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.70
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.72
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.30
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.18
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.00
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.87e-4
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.78
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.17
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4349.74
 p-value of test no 227                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4370.79
 p-value of test no 228                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.73
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.00
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.92
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000059788
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999987422
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 237                :    0.9952
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 241                :    0.9901
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:41.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197853195.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27055
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7141
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.65
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.29
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.87
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.14
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.61
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.90
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.90
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.95
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.50
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.25
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.39
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.54
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.70
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.34
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.11
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908370
   j =  2                              :            45809
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908174
   j =  2                              :            45907
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 88                 :  3.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.14
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.96
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.94
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.44
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.27
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.21
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.08
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.68
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.83
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.88
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.39
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.30
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.88
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.11
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.52
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.67
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.68
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.65
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.28
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.78
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.60
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.42
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.08
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.91
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.91
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.90
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.40
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.86
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.56
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.65
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.37
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.34
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.16
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.29
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.47
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.92
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.11
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.55
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.82
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.45
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.46
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.59
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.65
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.02
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3768.40
 p-value of test no 227                : 1 -  3.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.28
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.39
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11538.27
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.01
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999939677
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.56
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000149698
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  97  HammingIndep, L=300, r=0       1 -  3.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198803463.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27056
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 5                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5304
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    3.97
 p-value of test no 33                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.9910
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.02
 p-value of test no 47                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.96
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.95
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.00
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.23
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.90
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.87
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.23
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.38
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.39
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.31
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.86
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.83
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46203
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907596
   j =  2                              :            46199
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908568
   j =  2                              :            45713
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.99
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.99
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.24
 p-value of test no 121                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.88
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.75
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.24
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.74
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17675.94
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.86
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.81
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.95
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.54
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.33
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.71
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.15
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.63
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.71
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.00
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  590.23
 p-value of test no 158                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.64
 p-value of test no 159                :    0.9957
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.15
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.45
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.55
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.20
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.82
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.91
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.54
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.04
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.47
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.84
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.98
 p-value of test no 172                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.50
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.48
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.35
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.66
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.74
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.30
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.17
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.21
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.39
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.80
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.94
 p-value of test no 218                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.09
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.68
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.75
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.25
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.87
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.82
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.11
 p-value of test no 231                :  1.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000043552
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.03
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000067420
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:09.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199786503.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27057
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.38
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.19
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.26
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.76
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.72
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.76
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.48
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.72
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.63
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.89
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.48
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.13
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908173
   j =  2                              :            45906
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908102
   j =  2                              :            45940
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.89
 p-value of test no 117                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.06
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.95
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.71
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.16
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.00
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.08
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.62
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.69
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.15
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17200.80
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.51
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.72
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.91
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.34
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.13
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.91
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.41
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.91
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.55
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.87
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.48
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.61
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.11
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.35
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.40
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.98
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.91
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.05
 p-value of test no 165                :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.21
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.53
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.97
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.34
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.55
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.29
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.00
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.64
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.69
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.90
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.70
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.09
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 185                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 188                :  8.9e-3
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.09
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.35
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.76
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.61
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.22
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.17
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.89
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.06
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.23
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.00
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999947387
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.72
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999996398
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.28
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:06.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200769543.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27058
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 11                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7521
 p-value of test no 20                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.40
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.90
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.25
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.88
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.07
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.00
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.68
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.30
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.62
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.83
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.68
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.05
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.29
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908475
   j =  2                              :            45755
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907953
   j =  2                              :            46019
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.19
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.63
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.37
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.45
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.52
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.77
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.36
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.63
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.58
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.50
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.61
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.79
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.62
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.19
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.06
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.13
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.41
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.13
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.81
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.74
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.78
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.96
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.91
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.83
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.39
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.79
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.53
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.99
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.65
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.47
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.93
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.77
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.49
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.40
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.02
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.64
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.24
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.67
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.76
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.32
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.08
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.24
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.42
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12161.10
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.72
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.24
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999928130
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.83
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000162466
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:55.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201752583.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27059
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1247
 p-value of test no 11                 :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334367
   j =  1                              :        599997506
   j =  2                              :             1247
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5299
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7073
 p-value of test no 19                 :    0.9980
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7561
 p-value of test no 21                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.23
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.85
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.12
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.45
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.23
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.38
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.20
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.17
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7231.18
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.44
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 63                 :    0.9922
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.22
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.68
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.82
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908525
   j =  2                              :            45733
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908214
   j =  2                              :            45890
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.72
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.32
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.14
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.18
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.91
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.58
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.61
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.85
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.84
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17170.55
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.52
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.28
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.14
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.69
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.41
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.42
 p-value of test no 151                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.20
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.77
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.27
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.78
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  604.54
 p-value of test no 158                :  9.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.79
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.95
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.16
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.98
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.24
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.19
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.84
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.57
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.54
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.76
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.36
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.06
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.49
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.82
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.98
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.86
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.65
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.00
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.18
 p-value of test no 189                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.29
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.18
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.83
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.83
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.61
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.80e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.99
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.87
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.11
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.20
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.81
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.65
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.57
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000171163
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.92
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000156526
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:58:19.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9993 
  76  RandomWalk1 J (L=1000, r=0)     9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202964999.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27060
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4502
 p-value of test no 16                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.39
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.84
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.27
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.03
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.36
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.50
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.27
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.35
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.64
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.44
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.61
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4800.09
 p-value of test no 68                 :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907852
   j =  2                              :            46074
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908483
   j =  2                              :            45757
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 117                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.88
 p-value of test no 119                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.72
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.97
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.05
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.78
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.81
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.89
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.27
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.72
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.10
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.01
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.18
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.24
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.39
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.29
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.42
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.87
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.55
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.11
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.32
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.26
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.30
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.33
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.06
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.71
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.22
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.49
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.89
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.05
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.22
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.62
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.03
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.06
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.85
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.83
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.80
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.36
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.58
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.82
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.05
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.89
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.70
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.53
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.87
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.85
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.83
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.40
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.88
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.31
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000073075
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.56
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999947990
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 238                :    0.06
 
 Sample variance                       :    2.10
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:24.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183369740.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27061
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 3                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4144
 p-value of test no 17                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.83
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.73
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.17
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.68
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.34
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.01
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.32
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.23
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.96
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.51
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.35
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.01
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.19
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908471
   j =  2                              :            45760
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908136
   j =  2                              :            45923
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.95
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.05
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.32
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.43
 p-value of test no 122                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.69
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.15
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.22
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.12
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.94
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17091.77
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.32
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.46
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.87
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.24
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.42
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.06
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.64
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.15
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.16
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.50
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.80
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.15
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.98
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.28
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.53
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.30
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.48
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.08
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.16
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.40
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.46
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.17
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.50
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5245.58
 p-value of test no 173                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.82
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.70
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.65
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.71
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.34
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.03
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.26
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-4
 p-value of test no 213                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9639.59
 p-value of test no 215                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.10
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5085.30
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.12
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.68
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.33
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.74
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.95
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999928613
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.79
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000059149
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:29.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184090636.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27062
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5557
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.02
 p-value of test no 35                 :  8.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.88
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.63
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.46
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.91
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.01
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.39
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.16
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.21
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.12
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.41
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.87
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46226
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870226
   j =  1                              :        399907554
   j =  2                              :            46214
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46362
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870362
   j =  1                              :        399907277
   j =  2                              :            46360
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 92                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.24
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.13
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.59
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.80
 p-value of test no 122                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.69
 p-value of test no 123                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.65
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.18
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.28
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.11
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.40
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.65
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17680.89
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.70
 p-value of test no 146                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.49
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.24
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.40
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.61
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.08
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.19
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.86
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.61
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.89
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.60
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.53
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.08
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.41
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.68
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.66
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.95
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.59
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.09
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.07
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.81
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.71
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.35
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.61
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.18
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.35
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.70
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.07
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.37
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.00
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.48
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.22
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.02
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9757.20
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.97
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.60
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5116.18
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.45
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.01
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.91
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.06
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.34
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999927140
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.65
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000198517
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9921
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.86e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:20.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185204748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27063
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4521
 p-value of test no 14                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9920
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   22.20
 p-value of test no 47                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.41
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.34
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.59
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.73
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.88
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.22
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.30
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.29
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.95
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.78
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.52
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.20
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908562
   j =  2                              :            45713
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907959
   j =  2                              :            46016
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 76                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.06
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.23
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.21
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.79
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.63
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.80
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.72
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.19
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.56
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.56
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.54
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17218.22
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.85
 p-value of test no 146                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.47
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.72
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.95
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.00
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.90
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.34
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.32
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.67
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.02
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.97
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.62
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.89
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.81
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.69
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.73
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.92
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.05
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.89
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.80
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.33
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.24
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.93
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.62
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.53
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.80
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.58
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.61
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.73
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    2.76
 p-value of test no 184                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.22
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 204                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.55
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.71
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.47
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.55
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.27
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.77
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.85
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11592.88
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.43
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.08
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999907001
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.10
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999944369
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:48.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186220556.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27064
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7539
 p-value of test no 18                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    4.21
 p-value of test no 26                 :  6.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.84
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.50
 p-value of test no 50                 :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.21
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.22
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.11
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.98
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.04
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7288.43
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.14
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.46
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.72
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.11
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.20
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908563
   j =  2                              :            45711
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907749
   j =  2                              :            46118
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.77
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.48
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.24
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.36
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.37
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.74
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.94
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.77
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.49
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.37
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.70
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.51
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.48
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.88
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.18
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.24
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.82
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.82
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.80
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.91
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.19
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.97
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  583.70
 p-value of test no 158                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.21
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.63
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.68
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.32
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.90
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.41
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.57
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.91
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.23
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.11
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.08
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.38
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.17
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.20
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.40
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.51
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.83
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.36
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.22
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.63
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.42
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.93
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.44
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 224                :    0.9919
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4665.63
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.37
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.64
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.39
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.44
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.24
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999921647
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.60
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999975365
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187203596.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27065
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.95
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.96
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.44
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.32
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.12
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.70
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.81
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.98
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.63
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.63
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.28
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.86
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.93
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908204
   j =  2                              :            45895
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908481
   j =  2                              :            45752
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 100                :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    5.58
 p-value of test no 102                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.02
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.91
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.10
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.48
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.72
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.37
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.89
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.77
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.91
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17204.05
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.53
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.96
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.96
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.91
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.91
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.34
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.79
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.07
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.63
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.24
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.05
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.02
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.72
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.54
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.01
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.92
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.01
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.13
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.28
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.31
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.62
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.19
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.69
 p-value of test no 172                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5142.81
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.99
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.35
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.50
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.33
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.58
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.87
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.13
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.47
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.66
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.17
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4346.72
 p-value of test no 227                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.30
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.89
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.81
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.63
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999894272
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.17
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999880400
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.030
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:02.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188153868.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27066
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.80
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.17
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.13
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.42
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.53
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.12
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.45
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.17
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.78
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.58
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.76
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.74
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.11
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.89
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.65
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.73
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908285
   j =  2                              :            45850
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908221
   j =  2                              :            45885
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.89
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.60
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.80
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.28
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.04
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.99
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.11
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.89
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17402.93
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.24
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.06
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.47
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.47
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.11
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.44
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.08
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.67
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.96
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.16
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.59
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.65
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.69
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.35
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.49
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.56
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.56
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.47
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.08
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.04
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.47
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.22
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.34
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.97
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.36
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.28
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.41
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.69
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.93
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.08
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.24
 p-value of test no 198                :  6.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.30
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.63
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.22
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.36
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.43
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.70
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.58
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.67
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.64
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12235.23
 p-value of test no 230                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.62
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999765608
 
 Normal statistic for number of bits   :   -1.85
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.74
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000027058
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:16.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189169676.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27067
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9975
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    3.60
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.10
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.58
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.24
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.72
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.86
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.54
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.00
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.82
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.29
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.19
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.20
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.75
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.62
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.46
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908419
   j =  2                              :            45783
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907821
   j =  2                              :            46082
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 73                 :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.19e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.82
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.58
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.14
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.73
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.80
 p-value of test no 125                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.90
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.24
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.22
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.46
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.07
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.43
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.31
 p-value of test no 147                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.13
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.85
 p-value of test no 149                :    0.9900
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.59
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.98
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.16
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.28
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.71
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.04
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.72
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.19
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.76
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.89
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.00
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.72
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.17
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.80
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.69
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.44
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.03
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.39
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.26
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.55
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.09
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.44
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.63
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.42
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.42
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.68
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.78
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.88
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.18
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.40
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.75
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.77
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.57
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.39
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.36
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.06
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.59
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999929327
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.21
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000020122
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:15.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190218252.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27068
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 17                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7498
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    3.17
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    4.23
 p-value of test no 42                 :  6.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.42
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.24
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.38
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.70
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.24
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.59
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.04
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.68
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.58
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.91
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6865.96
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.50
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  7.0e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.90
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.69
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.88
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.16
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46283
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870283
   j =  1                              :        399907437
   j =  2                              :            46277
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907663
   j =  2                              :            46161
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.34
 p-value of test no 116                :  4.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.01
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.55
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.99
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.49
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.76
 p-value of test no 123                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.48
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.84
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.18
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.92
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.59
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.99
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.66
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.56
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.62
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.42
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.83
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.73
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.66
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.75
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.25
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.33
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.71
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.81
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.80
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.45
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.46
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.93
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.01
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.34
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.07
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.20
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.54
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.85
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.01
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.19
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.73
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.67
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.28
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.13
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.17
 p-value of test no 198                :  6.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.95
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.40
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.14
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10288.71
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.94
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.11
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.71
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3872.49
 p-value of test no 228                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.77
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11415.55
 p-value of test no 230                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.55
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000001399
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.22
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000117529
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -2.74e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:37.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               4.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191234060.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27069
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.34
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.06
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.25
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.02
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.95
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.54
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.52
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.89
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.76
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.88
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.44
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.62
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.92
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.31
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908077
   j =  2                              :            45960
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46197
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907609
   j =  2                              :            46191
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.51
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.92
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.61
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.81
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.28
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.87
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.92
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.30
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.42
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.75
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.68
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.50
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.31
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.68
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.35
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.16
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.58
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.01
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.01
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.60
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.92
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.42
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.61
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.17
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.95
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.63
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.91
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.58
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.46
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.59
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.88
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.06
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.33
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.79
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.52
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.20
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.39
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.93
 p-value of test no 176                :  2.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.90
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.57
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.91
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.63
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.90
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.24
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.15
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.35
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.06
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.94
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.95
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.24
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999929012
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.04
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999905681
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:50.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192380940.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27070
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 5                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4180
 p-value of test no 14                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.74
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    3.57
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.43
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.52
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.18
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.33
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.36
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.26
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.02
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.58
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.44
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.53
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.36
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.88
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907975
   j =  2                              :            45999
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908168
   j =  2                              :            45910
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 101                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.15
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.69
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.90
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.86
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.07
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.68
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.98
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17349.85
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.08
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.81
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.50
 p-value of test no 148                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.75
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.58
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.68
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.72
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.08
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.88
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.66
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.49
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.49
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.96
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.27
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.59
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.74
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.47
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.90
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.40
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.76
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.50
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.75
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.35
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.99
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.61
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.95
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.89
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.77
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.61
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.11
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.18
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.84
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.83
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.61
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.94
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.16
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.85
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3901.41
 p-value of test no 227                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.66
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.84
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.33
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.58
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000084166
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.02
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999956222
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 241                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:02.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193396748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27071
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 10                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    3.67
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.54
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.39
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.47
 p-value of test no 52                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.36
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.71
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.85
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.07
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.91
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.23
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.70
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4926.32
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45981
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908043
   j =  2                              :            45971
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908328
   j =  2                              :            45830
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.61
 p-value of test no 118                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.37
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.32
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.07
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.73
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.72
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.53
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.85
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.03
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.63
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17124.75
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.19
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.49
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.12
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.77
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.48
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.07
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.20
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.09
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.94
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.68
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.24
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.70
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.75
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.10
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.72
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.23
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.15
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.62
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.48
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.38
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.79
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.50
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.05
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.41
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.93
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.66
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.46
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  145.03
 p-value of test no 175                :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.43
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.06
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    5.23
 p-value of test no 202                :  2.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  267.77
 p-value of test no 203                :  9.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.35
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.00
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.84
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
 p-value of test no 220                :    0.9957
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4700.45
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 223                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4667.36
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.69
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.70
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.39
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.30
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.99
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000004486
 
 Normal statistic for number of bits   :   0.035
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.13
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999876029
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    2.93
 p-value of test no 244                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 250                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 252                :  3.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.82
 p-value of test no 253                :    0.9976
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:37.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9995 
  58  AppearanceSpacings, r = 27      0.9998 
  88  PeriodsInStrings, r = 0         9.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194314252.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27072
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 8                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 11                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    3.15
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.85
 p-value of test no 41                 :  3.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.22
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.91
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.38
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.99
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.06
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.18
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.09
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.74
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.59
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7353.85
 p-value of test no 57                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.43
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.76
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.82
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.83
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908319
   j =  2                              :            45836
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907958
   j =  2                              :            46012
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.08
 p-value of test no 119                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.70
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.49
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.59
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.49
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.86
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.24
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.12
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.20
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.08
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.87
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.21
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.48
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.42
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.02
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.26
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.00
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.04
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.25
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.41
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.34
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.51
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.59
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.07
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.88
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.03
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.58
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.13
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.92
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.95
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.15
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.63
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.11
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.36
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.73
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.45
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4672.17
 p-value of test no 173                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.69
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.71
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.22
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.82
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.19
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.19
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.66
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.39
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5105.34
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.18
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.45
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.09
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.26
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.86
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.64
 p-value of test no 231                :  3.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999978701
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.78
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999947876
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.085
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:13.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7            0.9990 
  79  RandomWalk1 J (L=10000, r=15)   0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195297292.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27073
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 7                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.98
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.61
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.13
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.03
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.16
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.64
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.61
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.49
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.17
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.19
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.48
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.23
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4888.81
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908353
   j =  2                              :            45822
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908181
   j =  2                              :            45902
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 117                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.88
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.30
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.66
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.86
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.39
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.00
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.73
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.06
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.68
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17649.76
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.97
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.08
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.60
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.72
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.21
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.51
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.12
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.35
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.74
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.01
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.35
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.51
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.37
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.13
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.76
 p-value of test no 161                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.14
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.46
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.34
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.92
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.87
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.54
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.52
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.02
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.91
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.11
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.35
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.79
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.98
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.24
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.67
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.05
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.25
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.11
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.70
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.98
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.59
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.70
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3875.42
 p-value of test no 227                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.37
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.50
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.03
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.04
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000059710
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.97
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000074551
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:54.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196313100.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27074
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 34                 :    0.9965
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.70
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.79
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.76
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.48
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.09
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.21
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.53
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.58
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.26
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.08
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.24
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.64
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.29
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.38
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.76
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908227
   j =  2                              :            45879
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908256
   j =  2                              :            45863
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.38
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.92
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.00
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.39
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.25
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.70
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.50
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 131                :    0.9952
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 132                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.53
 p-value of test no 133                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.43
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17631.43
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.36
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.66
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.73
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.08
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.16
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.35
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.12
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.06
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.52
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.54
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.56
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.42
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.50
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.21
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.20
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.64
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.49
 p-value of test no 166                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.97
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.83
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.90
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.10
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.28
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.82
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.43
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.22
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.34
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.85
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.35
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.93
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
 p-value of test no 201                :    0.9970
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  151.26
 p-value of test no 203                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.28
 p-value of test no 207                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.52
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.07
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.13
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.61
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.60
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.65
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.05
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11627.40
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.13
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999930296
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.25
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999900131
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:58.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197328908.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27075
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 3                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7094
 p-value of test no 18                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.91
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.78
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.62
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.76
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.17
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.61
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.63
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.70
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.84
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.49
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4944.23
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45499
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869499
   j =  1                              :        399909007
   j =  2                              :            45489
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.52
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.40
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  109.80
 p-value of test no 121                :  7.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.82
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.71
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.62
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.68
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.01
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.19
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17531.61
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.40
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.74
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.09
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.41
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.03
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.98
 p-value of test no 153                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.30
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.77
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.43
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.81
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.57
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.63
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.35
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.01
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.20
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.34
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.75
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5223.02
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.57
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.78
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.79
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.38
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4789.34
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.74
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.44
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.20
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.95
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    2.29
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.47
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.50
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.61
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.97
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.75
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.04
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.45
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.14
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.96
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.85
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.87
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999949286
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.07
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000000340
 
 Normal statistic for number of bits   : 2.69e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:53.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  61  WeightDistrib, r = 28           7.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198311948.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27076
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.04
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.32
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.25
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.57
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.84
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.51
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.83
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.79
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.85
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.91
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.78
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.88
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.47
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.49
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908091
   j =  2                              :            45947
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46159
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907686
   j =  2                              :            46151
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.24
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.96
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.75
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.25
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.28
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.23
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.21
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.10
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.35
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.32
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.12
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.86
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.79
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.67
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.84
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.61
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.91
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.12
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.90
 p-value of test no 153                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.48
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.28
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.46
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.67
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.11
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.62
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.61
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.83
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.34
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.29
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.68
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.63
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.91
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.55
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.03
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.67
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.35
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.84
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.92
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.39
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.06
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 185                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-4
 p-value of test no 186                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 187                :  8.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.95
 p-value of test no 188                :    0.9984
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.46
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.96
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.32
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.89
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.15
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.67
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.71
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.57
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.45
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.44
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.61
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.83
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000062539
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.98
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000220633
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:08.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199327756.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27077
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 3                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 9                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9928
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.86
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.72
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.93
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.89
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.76
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.02
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.83
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.60
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.95
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.32
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.74
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.50
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.97
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.49
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4796.72
 p-value of test no 68                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46245
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870245
   j =  1                              :        399907514
   j =  2                              :            46237
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908525
   j =  2                              :            45730
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.56
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.47
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.07
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.42
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.54
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.71
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.73
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.81
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.24
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 139                :    0.9934
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.17
 p-value of test no 141                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17442.28
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.11
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.01
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.20
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.83
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.16
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.01
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.34
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.36
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.40
 p-value of test no 154                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.94
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.63
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.36
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.37
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.08
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.10
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.83
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.69
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.29
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.16
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.57
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.91
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.04
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.19
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.03
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.14
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.13
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.35
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.87
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.02
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.13
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.27
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.91
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10230.76
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.88
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.98
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.54
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.57
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11617.28
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.82
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.65
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000020530
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.93
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999970634
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    2.03
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:02.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200343564.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27078
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.67
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.81
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.92
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.01
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.94
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.90
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.92
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.17
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.94
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.33
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.39
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.13
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.09
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.78
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.72
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908056
   j =  2                              :            45969
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908324
   j =  2                              :            45835
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.69
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.04
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.85
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.93
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.87
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.07
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.41
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.33
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.13
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.48
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.77
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.16
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.41
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.67
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.88
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.97
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.42
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.70
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.36
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.27
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.93
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.04
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.47
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.79
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.77
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.43
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.27
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.03
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.99
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.82
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.09
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.98
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.79
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.02
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.99
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.40
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.26
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.05
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.13
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.25
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.63
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.39
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.40
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 221                :    0.9967
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.36
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.16
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.04
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.75
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.93
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.66
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.01
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999964451
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.51
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000067171
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:09.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201359372.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27079
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.05
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.70
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.56
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.31
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.55
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.32
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.68
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.29
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.02
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.26
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7218.23
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.04
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.92
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.73
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.13
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4841.32
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907892
   j =  2                              :            46048
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907857
   j =  2                              :            46064
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.01
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.04
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.24
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.00
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.82
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.45
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.60
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.43
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.21
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17159.70
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.16
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.84
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.03
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.85
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.92
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.21
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.87
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.74
 p-value of test no 156                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.82
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.77
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.24
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.10
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.56
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.31
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.63
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.52
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.26
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.38
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.94
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.68
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.52
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.87
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.29
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.82
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.17
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.49
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.35
 p-value of test no 179                :  9.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.30
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.25
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.33
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.78
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.80
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.97
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.37
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.14
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.84
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.24
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12352.51
 p-value of test no 230                :  3.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000069031
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999972188
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:43.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202309644.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27080
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.46
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.12
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.01
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.28
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.86
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.97
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.63
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7225.47
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.77
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.62
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.91
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.33
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4810.85
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908523
   j =  2                              :            45737
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908453
   j =  2                              :            45769
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 83                 :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.17
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.34
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.05
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.00
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.57
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.86
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.61
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.02
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.86
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.72
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17548.88
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.16
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.59
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.69
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.29
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.00
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.26
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.90
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.05
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.23
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.92
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.05
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.14
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.29
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.15
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.74
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.53
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.42
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.41
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.74
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.34
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.75
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.18
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.02
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.64
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.22
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.29
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.18
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.29
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.33
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.37
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.21
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.47
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.76
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.38
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.17
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.45
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10303.92
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.60
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.13
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.24
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.38
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.15
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.03
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.23
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999990275
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.66
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000058714
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 240                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.26
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 250                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 252                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.72
 p-value of test no 253                :    0.9967
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:22.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183402509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27081
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5532
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.61
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.26
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.80
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.60
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.67
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  288.32
 p-value of test no 54                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.04
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.26
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.91
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.23
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 62                 :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  7.0e-3
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   95.78
 p-value of test no 65                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.27
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.29
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5164.88
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908493
   j =  2                              :            45746
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907993
   j =  2                              :            45999
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.54
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.28
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.54
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.19
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.77
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.07
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.09
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.97
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.70
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.24
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.97
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.47
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.38
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.40
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.16
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.35
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.63
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.89
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.91
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.97
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.38
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.61
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.88
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.20
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.24
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.82
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.41
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.05
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.85
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.49
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.37
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.67
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.68
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.23
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.29
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.24
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.37
 p-value of test no 196                :  4.3e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.08
 p-value of test no 198                :    0.9977
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.88
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.18
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.73
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.53
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.05
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.45
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.28
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.35
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.08
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.29
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.55
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999994286
 
 Normal statistic for number of bits   :  -0.045
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.35
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000022132
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:54.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184680461.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27082
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.24
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.32
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.16
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.15
 p-value of test no 52                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.05
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.04
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.69
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.47
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6867.05
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.97
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.17
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.18
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.63
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.64
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908015
   j =  2                              :            45985
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907710
   j =  2                              :            46139
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 100                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.70
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.44
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.92
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.64
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.08
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.20
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.09
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.92
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.02
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17650.00
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.78
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.15
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.08
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.44
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.92
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.38
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.92
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.68
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.86
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.87
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.60
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.06
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.22
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.42
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.35
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.45
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.10
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.07
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.05
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.60
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.95
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.04
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.47
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.58
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.37
 p-value of test no 198                :    0.9947
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.29
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.97
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.98
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.63
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.71
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4695.99
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.31
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.30
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.67
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.93
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.72
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999978026
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.22
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000028606
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.053
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:17.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185532429.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27083
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.29
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.51
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.98
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.47
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.82
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.79
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.29
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.09
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.53
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.48
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.95
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.90
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908586
   j =  2                              :            45704
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908492
   j =  2                              :            45745
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 74                 :    0.9946
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.15
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.86
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.77
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.45
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.86
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.15
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.84
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.16
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.10
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.91
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.69
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.21
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.46
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.53
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.34
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.54
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.88
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.61
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.46
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.73
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.29
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.89
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.77
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.70
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.00
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.22
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.14
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.30
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.45
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.55
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.39
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.81
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.34
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.99
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.70
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.34
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.16
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.52
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.06
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.22
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.13
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.50
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.76
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.87
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.99
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.03
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.33
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.95
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12164.91
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.85
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000136585
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.78
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000027493
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9948
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.085
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:22.09
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186515469.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27084
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.84
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.80
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.46
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.91
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.43
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.15
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.99
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.82
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.67
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.99
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.68
 p-value of test no 59                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 60                 :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   56.10
 p-value of test no 61                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.41
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.98
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.58
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.07
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907711
   j =  2                              :            46140
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46257
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870257
   j =  1                              :        399907489
   j =  2                              :            46251
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.34
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.72
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.49
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.38
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.44
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.61
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.60
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.71
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.66
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17236.09
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.78
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.44
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.05
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.66
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.69
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.44
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.45
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.14
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.55
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.28
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.08
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.70
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.16
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.06
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.41
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.96
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.47
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.92
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.39
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.45
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.23
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.09
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.51
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.72
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.03
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.47
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.51
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.33
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.20
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.15
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.59
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.53
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.68
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.24
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.98
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.94
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.19
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.75
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.46
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.96
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.69
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000148627
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.17
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999921407
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 243                :  9.7e-3
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:17.84
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187465741.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27085
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7537
 p-value of test no 20                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.98
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.89
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.53
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.04
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.18
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.28
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.12
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.09
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.12
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.78
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.92
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.82
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.63
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.56
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908207
   j =  2                              :            45889
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908594
   j =  2                              :            45691
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.57
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.43
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.34
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.50
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.33
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.04
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.23
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.29
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 138                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  173.46
 p-value of test no 141                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.52
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.18
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.42
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.09
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.22
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.38
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.64
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.26
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.44
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.34
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.70
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.64
 p-value of test no 156                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.03
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.81
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.11
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.60
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.69
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.56
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.72
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.42
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.24
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.97
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.03
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.17
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.05
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.67
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.62
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.73
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.00
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.79
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.63
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.60
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.48
 p-value of test no 177                :    0.9935
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.26
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 187                :    0.9992    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.81
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.46
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.83
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.99
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4732.68
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.62
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.32
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.45
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.66
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.29
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.12
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999880364
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.24
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000157729
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.017
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:36.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188448781.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27086
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    4.22
 p-value of test no 33                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.91
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.70
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.05
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.19
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.85
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.03
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.38
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.56
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.62
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.60
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.11
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.91
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.58
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908121
   j =  2                              :            45938
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907942
   j =  2                              :            46026
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.95
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.40
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.67
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.29
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.64
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.43
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.97
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.71
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.09
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.13
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.52
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.37
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.43
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.85
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.76
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.25
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.92
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.45
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.41
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.53
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.79
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.49
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.26
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.94
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.42
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.27
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.29
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.03
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.47
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.27
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.46
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.37
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.90
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.63
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.50
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.65
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.73
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.96
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.98
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.83
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.21
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.57
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.53
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.15
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.74
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.22
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.18
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.55
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.46
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.24
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000154378
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.43
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999908429
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:53.61
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189333517.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27087
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.53
 p-value of test no 28                 :  5.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.63
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.21
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.47
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.94
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.89
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.39
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.11
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.79
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.38
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.65
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.31
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.05
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.12
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.08
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908192
   j =  2                              :            45895
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907775
   j =  2                              :            46111
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 74                 :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.9916
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.21
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.99
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.48
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.89
 p-value of test no 122                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.72
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.14
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.22
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.53
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 131                :    0.9951
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.40
 p-value of test no 133                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.56
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 142                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17895.05
 p-value of test no 145                :  6.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.93
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.60
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.34
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.22
 p-value of test no 150                :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.21
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.46
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.72
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.50
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.63
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.74
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.64
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.55
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.52
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.87
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.03
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.06
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.78
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.47
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.70
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.72
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5214.79
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.00
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.95
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.07
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.53
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.78
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.48
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.10
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.00
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.04
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.85
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.67
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.38
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.78
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.11
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.84
 p-value of test no 216                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.35
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.35
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.78
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.56
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.68
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.23
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.20
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999855251
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.61
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000180085
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.20
 p-value of test no 254                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:04.76
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190316557.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27088
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5552
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 26                 :    0.9972
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.76
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.41
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.48
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.74
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.76
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.68
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.97
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.51
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.03
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.29
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.88
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.50
 p-value of test no 67                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.05
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908470
   j =  2                              :            45762
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908315
   j =  2                              :            45838
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.17
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.04
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.09
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.50
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.64
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.52
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.82
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.96
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.10
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17129.89
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.73
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.37
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.77
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.84
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.86
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.50
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.38
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.33
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.99
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.02
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.42
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.89
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.61
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.34
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.07
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.84
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.95
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.00
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.37
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.65
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.66
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.05
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.05
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.50
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.46
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.00
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.73
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.33
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.12
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.81
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.28
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.08
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 214                :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9646.17
 p-value of test no 215                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.43
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.78
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.53
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.97
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.96
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.96
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.18
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999958250
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.82
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999917891
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 240                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.86
 p-value of test no 243                :  2.1e-3
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:06.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191332365.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27089
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.42
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.48
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.11
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.68
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.77
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.07
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.78
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7211.93
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.18
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.78
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.21
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.76
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907687
   j =  2                              :            46140
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45579
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869579
   j =  1                              :        399908845
   j =  2                              :            45573
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.19
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.72
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.24
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.23
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.90
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.88
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.10
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.26
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.25
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.37
 p-value of test no 135                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.77
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17724.01
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.45
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.90
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.36
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.67
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.96
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.17
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.73
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.22
 p-value of test no 154                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.88
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.45
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.88
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.30
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.10
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.68
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.77
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.14
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.29
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.78
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.53
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.91
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.44
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.75
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.04
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.91
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.20
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.32
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.18
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.74
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.91
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.49
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.65
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.39
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.44
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.69
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9736.52
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.89
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.83
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.08
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.62
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.60
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.58
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.49
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000025048
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.14
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999948491
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:53.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192348173.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27090
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 6                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9937
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.90
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.90
 p-value of test no 47                 :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.76
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.19
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.38
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.93
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  372.18
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.83
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.07
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.65
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.77
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.66
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.05
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908561
   j =  2                              :            45715
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907938
   j =  2                              :            46025
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
 p-value of test no 72                 :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 73                 :  7.8e-4    *****
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 74                 :  2.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  1.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.73
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.63
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.09
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.54
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.39
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.40
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.73
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.44
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.53
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17209.88
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.79
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.80
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.52
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.15
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.84
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.51
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.78
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.95
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.67
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.65
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.48
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.16
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.75
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.94
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.97
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.19
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.58
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.53
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.95
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.78
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.52
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.26
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.38
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.64
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.91
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.29
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.60
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.91
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.92
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.85
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.02
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.48
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.94
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.02
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.64
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.93
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.19
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.60
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.59
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000009859
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.97
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999912614
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.56
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193363981.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27091
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.15
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.60
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   42.22
 p-value of test no 48                 :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.34
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.58
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.98
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.73
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.72
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.38
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.01
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.68
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.40
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.35
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.30
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.11
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.69
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908625
   j =  2                              :            45677
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908692
   j =  2                              :            45651
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.70
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.84
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.38
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.50
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.06
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.62
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.43
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.09
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.58
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17550.99
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.03
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.99
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.78
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.61
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.00
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.51
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.49
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.43
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.03
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.42
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.98
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.48
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.54
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.04
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.71
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.14
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.79
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.28
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.63
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.98
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.79
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.97
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.12
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.67
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.94
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.67
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.01
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.14
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.15
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.14
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10217.32
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.15
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.03
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.24
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.17
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11543.76
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11351.02
 p-value of test no 230                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.73
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000020554
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.54
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999928748
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:18.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194281485.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27092
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.57
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.55
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.83
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.56
 p-value of test no 53                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.94
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.76
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.38
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7227.31
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.28
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.70
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.54
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.72
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.27
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908063
   j =  2                              :            45964
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908232
   j =  2                              :            45881
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 91                 :    0.9951
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 101                :    0.9932
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 106                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    7.33
 p-value of test no 108                :  2.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.44
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.38
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.30
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.88
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.28
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.03
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.90
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.85
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.38
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.31
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.34
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.16
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.58
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.57
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.66
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.46
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.85
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.96
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.70
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.12
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.07
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.16
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.20
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.84
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.52
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.43
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.85
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.90
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.12
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.05
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.41
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.06
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.83
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.08
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.65
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.73
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.10
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.16
 p-value of test no 178                :    0.9943
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 185                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    5.27
 p-value of test no 187                :  2.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.00
 p-value of test no 188                :    0.9986
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.20
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.57
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.78
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.54
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.01
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.06
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.10
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.24
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.43
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.97
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.14
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999984548
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.27
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000137209
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:41.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  52  SampleProd, t = 24              2.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195362829.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27093
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 11                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.95
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.37
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.94
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.77
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.37
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.59
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.90
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.57
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.93
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.12
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.04
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.49
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.71
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907785
   j =  2                              :            46103
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908250
   j =  2                              :            45869
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 72                 :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
 p-value of test no 76                 :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 78                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.95
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.28
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.42
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.07
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.12
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.52
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.99
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.37
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.99
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.01
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.19
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.42
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.31
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.67
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.96
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.54
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.07
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.29
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.31
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.54
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.17
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.95
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.90
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.13
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.04
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.17
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.97
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.67
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.55
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.86
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.24
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.97
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.72
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.50
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.65
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.74
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.50
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.68
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.09
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.06
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.81
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.77
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.16
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.42
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.62
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.66
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.73
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.55
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.83
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.11
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999938960
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.11
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000006808
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:21.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196378637.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27094
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9937
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.40
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.85
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.25
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.45
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.05
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.50
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.85
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.29
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.74
 p-value of test no 59                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 60                 :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   53.15
 p-value of test no 61                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.18
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.46
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.60
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908068
   j =  2                              :            45957
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908309
   j =  2                              :            45841
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.31
 p-value of test no 119                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.46
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.87
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.17
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.34
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.58
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.87
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.14
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.82
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.69
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.82
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.93
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.65
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.33
 p-value of test no 152                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.22
 p-value of test no 155                :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.27
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.02
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.39
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.63
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.65
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.29
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.87
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.76
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.08
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.75
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.08
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.47
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.10
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.91
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.07
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.10
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.08
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.50
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.20
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.68
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.14
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.85
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.41
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.99
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.28
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.75
 p-value of test no 218                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.86
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.56
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.78
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.40
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.18
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.62
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.57
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999968066
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999808415
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.34e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:55.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197394445.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27095
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.36
 p-value of test no 23                 :  2.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    3.75
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.70
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.32
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.24
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.08
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.55
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.81
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.46
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1555.00
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.89
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.68
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.59
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.49
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.11
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.93
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908468
   j =  2                              :            45766
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907998
   j =  2                              :            45998
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.52e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.85
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.63
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.93
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.82
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.13
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.68
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.60
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.72
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.22
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.49
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.62
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.46
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.77
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.52
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.06
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.27
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.41
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.08
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.09
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.32
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.58
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.92
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.94
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.24
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.22
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.26
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.91
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.93
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.42
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.95
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.03
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.02
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.10
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.47
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.75
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.22
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.71
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.12
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 188                :    0.97
 
 Sample variance                       :    2.75
 p-value of test no 189                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.48
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.16
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.18
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.49
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.82
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.17
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.47
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.96
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.43
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.88
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.39
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.65
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000107449
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.87
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000018535
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:24.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198377485.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27096
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.89
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.28
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.36
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.83
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.63
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.02
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.92
 p-value of test no 53                 :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.05
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.92
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.96
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6880.02
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.03
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.57
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.95
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.77
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908646
   j =  2                              :            45671
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-4
 p-value of test no 87                 :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9945
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.98
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.76
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.79
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.74
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.92
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.76
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.67
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.54
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.18
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.23
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17598.56
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.23
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.03
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.50
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.89
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.86
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.95
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.90
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.72
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.78
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.89
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.24
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.45
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.39
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.40
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.28
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.81
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.53
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.66
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.11
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.63
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.39
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.43
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.87
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.91
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.30
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.36
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.19
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.22
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.49
 p-value of test no 176                :    0.9910
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 185                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.00
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.27
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.10
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.00
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.95
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.85
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.29
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.19
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.70
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.94
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.37
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.84
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.21
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999958409
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.80
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000125611
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.26
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199458829.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27097
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    3.08
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.41
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.57
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.81
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.45
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.03
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.61
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.74
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.94
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.56
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.89
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.02
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.88
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.74
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.82
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.25
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907923
   j =  2                              :            46037
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908081
   j =  2                              :            45958
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.85
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.97
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.07
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.74
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.41
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.65
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.08
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.90
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.09
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.25
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.01
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.25
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.70
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.61
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.08
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.46
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.77
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.79
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.76
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.83
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.41
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.79
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.03
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.26
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.49
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.30
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.58
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.23
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.17
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.23
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.89
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.34
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.44
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.28
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.56
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.68
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.59
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.95
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 185                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.61
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.98
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.87
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 212                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 214                :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9652.87
 p-value of test no 215                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.29
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.22
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.26
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.00
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.06
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.93
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.29
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000206629
 
 Normal statistic for number of bits   :    1.63
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.67
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000095026
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9903
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    2.28
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:41.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200474637.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27098
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.08
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.47
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.84
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.89
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.32
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.35
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.22
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.39
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6925.99
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.24
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.20
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.72
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.13
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.42
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907716
   j =  2                              :            46136
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45567
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869567
   j =  1                              :        399908870
   j =  2                              :            45559
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.14
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.47
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.38
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.33
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.68
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.10
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.80
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.27
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.03
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.42
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.74
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.35
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.68
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.46
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.35
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.35
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.28
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.51
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.80
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.92
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.93
 p-value of test no 157                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.99
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.31
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.63
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.67
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.20
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.64
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.48
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.24
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.14
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.88
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.37
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.13
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.90
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.20
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.57
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.11
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.18
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.69
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.36
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.14
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.29
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.91
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.67
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.38
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.52
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.16
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.44
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.93
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.74
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.15
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000064480
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.70
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000021922
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:03.76
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201523213.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27099
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.00
 p-value of test no 28                 :  8.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.60
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.84
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.35
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.25
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.27
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.18
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.11
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.15
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.91
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.08
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  199.88
 p-value of test no 67                 :  5.0e-6    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.31
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908174
   j =  2                              :            45907
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907910
   j =  2                              :            46036
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.83
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.92
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.82
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.80
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.96
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.04
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.43
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.72
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.28
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.42
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.83
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.08
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.31
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.81
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.25
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.60
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.76
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.95
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.79
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.42
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.51
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.66
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.37
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.86
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.13
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.33
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.50
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.49
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.20
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.34
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.36
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.65
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.70
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.74
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.53
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.58
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.34
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.72
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.96
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.41
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.13
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.67
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.06
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.50
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.31
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.62
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.17
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 223                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4647.67
 p-value of test no 226                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.37
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3911.51
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.30
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.58
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.74
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000078931
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.24
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999991583
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:00:51.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              5.0e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202637325.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27100
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.55
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.16
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.19
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.78
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.97
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.99
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.29
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.45
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.71
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.37
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.17
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5252.24
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908402
   j =  2                              :            45796
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908207
   j =  2                              :            45895
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.47
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.99
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.12
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.61
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.12
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.60
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.21
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.97
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.27
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17279.65
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.94
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.40
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.87
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.25
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.40
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.60
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.14
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.96
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.90
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.32
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.69
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.15
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.39
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.20
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.78
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.27
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.45
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.84
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.58
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.99
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.34
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.84
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.67
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.53
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.92
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.57
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.69
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.50
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.09
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.24
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.27
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.48
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.29
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 209                :  5.7e-4    *****
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 210                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10371.51
 p-value of test no 211                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.57
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.74
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.30
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.00
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.72
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.83
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.43
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.48
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000074794
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.91
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000131419
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 246                :    0.9999    *****
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:15:25.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183435278.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27101
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.00
 p-value of test no 46                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.46
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.13
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.13
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.33
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.83
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.30
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.23
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.03
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.22
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.06
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.73
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.96
 p-value of test no 66                 :  4.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.37
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.44
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908030
   j =  2                              :            45979
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907950
   j =  2                              :            46022
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-4
 p-value of test no 97                 :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.44
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.15
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.96
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.52
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.04
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.21
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.30
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.83
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.99
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.44
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17274.16
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.89
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.62
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.55
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.23
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.14
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.91
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.45
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.46
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.83
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.89
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.69
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.14
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.48
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.77
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.89
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.08
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.45
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.03
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.05
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.19
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.33
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.55
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.49
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.55
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.23
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.19
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.69
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.66
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 220                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 221                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5138.61
 p-value of test no 222                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.79
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.97
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.98
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.32
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.83
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.61
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000068077
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000054562
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:21.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184418318.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27102
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.72
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.12
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.22
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.65
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.79
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.99
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.97
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.83
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.27
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.58
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.82
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.89
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.73
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.15
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907987
   j =  2                              :            45999
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907572
   j =  2                              :            46208
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.11
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.46
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.63
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.01
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.95
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.28
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 131                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.79
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.30
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.52
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.35
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.83
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.92
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.74
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.02
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.32
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.15
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.21
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.43
 p-value of test no 155                :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.86
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.12
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.24
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.99
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.46
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.81
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.65
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.64
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.52
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.28
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.95
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.25
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.37
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.61
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.67
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.02
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.26
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.82
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.83
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.91
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.68
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.83
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.09
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.14
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.15
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.24
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.83
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.78
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.63
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.53
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11552.55
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11540.46
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.55
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999930851
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.52
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999968810
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 235                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 241                :    0.9938
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:31.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185270286.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27103
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 9                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 12                 :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 32                 :    0.9985
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.05
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.27
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.13
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.20
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.19
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.55
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.83
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.08
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.29
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.18
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.86
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.52
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.13
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.40
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907799
   j =  2                              :            46093
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45527
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869527
   j =  1                              :        399908951
   j =  2                              :            45517
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.49
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.52
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.13
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.37
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.48
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.36
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.57
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.10
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.27
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.55
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.72
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.97
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.12
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.03
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.90
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.38
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.88
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.90
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.45
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.05
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.95
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.82
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.10
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.30
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.63
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.91
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.98
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.28
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.41
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.27
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.20
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.11
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.40
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.91
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.91
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.31
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.15
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  254.51
 p-value of test no 203                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.07
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.72
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 213                :    0.9923
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9837.78
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.56
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.09
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.81
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.39
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12041.28
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.80
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000123709
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.94
 p-value of test no 233                :  4.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999984971
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186253326.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27104
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 10                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.59
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    3.23
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.26
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.41
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.70
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.92
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.87
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.55
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.07
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.09
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.04
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.70
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.36
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.27
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.85
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.94
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45517
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869517
   j =  1                              :        399908970
   j =  2                              :            45509
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907922
   j =  2                              :            46033
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.53
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.57
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.08
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.07
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.10
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.88
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.71
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.22
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.63
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.77
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.73
 p-value of test no 147                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.05
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.42
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.87
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.52
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.27
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.44
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.36
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.02
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.74
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.54
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.64
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.99
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.34
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.75
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.86
 p-value of test no 165                :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.65
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.89
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.64
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.83
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.07
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.21
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.85
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.79
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.61
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.17
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.57
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.04
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.62
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.95
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.62
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10190.42
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.85
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.04
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.84
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.32
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.11
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.37
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.98
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.47
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000042283
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.94
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000024877
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:52.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187269134.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27105
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.74
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.03
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.77
 p-value of test no 48                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.60
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.75
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.87
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.41
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.28
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.60
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.11
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.67
 p-value of test no 58                 :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 60                 :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.50
 p-value of test no 61                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.84
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.30
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.94
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907708
   j =  2                              :            46143
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907758
   j =  2                              :            46115
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.44
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.93
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.84
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.15
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.97
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.49
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.25
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.78
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17220.26
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.83
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.87
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.47
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.90
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.94
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.15
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.18
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.48
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.89
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.72
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.11
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.68
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.59
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.36
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.80
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.59
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.67
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.06
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.46
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.76
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.88
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.30
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.11
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.72
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.57
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.09
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.74
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.67
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.39
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.75
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.63
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.03
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.64
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.81
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.33
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.57
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9626.12
 p-value of test no 215                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.32
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.08
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.87
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.78
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.73
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.31
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.50
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000083188
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.97
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000009670
 
 Normal statistic for number of bits   :   0.076
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:08.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188186638.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27106
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 10                 :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.12
 p-value of test no 33                 :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.46
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.06
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.18
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.59
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.25
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.56
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.29
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.21
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 59                 :    0.9917
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.89
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.77
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.00
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.23
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908041
   j =  2                              :            45969
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908642
   j =  2                              :            45676
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.81
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.18
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.89
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.54
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.02
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.37
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.59
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.10
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.49
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.42
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16974.75
 p-value of test no 145                :    0.9930
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.59
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.44
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.15
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.57
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.48
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.13
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.17
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.33
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.07
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.48
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.98
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.13
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.81
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.45
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.13
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.10
 p-value of test no 162                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.30
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.64
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.55
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.09
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.10
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.45
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.07
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.22
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.89
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.92
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.57
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.93
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.05
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.86
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.68
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.33
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.34
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.55
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9698.35
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.39
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.21
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.61
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.00
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.53
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.36
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.76
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999919454
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.75
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999961850
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.066
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.96
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:28.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189202446.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27107
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.38
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.06
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.44
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.97
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.77
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.79
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.85
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.12
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.79
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.52
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.14
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.62
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.09
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908275
   j =  2                              :            45861
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907771
   j =  2                              :            46110
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-6
 p-value of test no 109                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.58
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.00
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.26
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.70
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.02
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.34
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.00
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.32
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.64
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.11
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.01
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.72
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.92
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.33
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.91
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.13
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.58
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.04
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.41
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.03
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.96
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.35
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.93
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.09
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.47
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.19
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.03
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.88
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.70
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.91
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.25
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.81
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.51
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.46
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.23
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.66
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.99
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.56
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 183                :    0.9903
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.64
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.76
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.26
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.03
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.79
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.80
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.06
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.92
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.12
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.28
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.20
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.40
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999971711
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.75
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999995528
 
 Normal statistic for number of bits   :  -0.035
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 253                :    0.9905
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:49.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190152718.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27108
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.58
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.08
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.94
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.03
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.26
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.78
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.75
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.06
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.70
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7156.15
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.95
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.26
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.36
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.59
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4932.88
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908662
   j =  2                              :            45666
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908460
   j =  2                              :            45761
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-5
 p-value of test no 113                :    0.9948
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.18
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.86
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.19
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.80
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.67
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.72
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.61
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.22
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.23
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.40
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.82
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17443.78
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.35
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.81
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.00
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.73
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.62
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.03
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.22
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.97
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.15
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.95
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.71
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.92
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.78
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.23
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.28
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.24
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.28
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.86
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.59
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.85
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.39
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.36
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.24
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.09
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.55
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.62
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.40
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.13
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.14
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.35
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 216                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.80
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.12
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.19
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.77
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12091.45
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.55
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.62
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999917216
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.69
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999879635
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:32.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191168526.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27109
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 7                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.93
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.07
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.28
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.55
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.95
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.64
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.95
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.47
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.65
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.31
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.92
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.62
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.34
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.12
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4902.69
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908534
   j =  2                              :            45730
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.26
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.82
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.08
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.75
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.59
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.53
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.21
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.88
 p-value of test no 134                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.93
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17755.45
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.28
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.05
 p-value of test no 147                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.27
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.69
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.94
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.90
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.67
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.86
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.73
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.85
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.23
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.50
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.15
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.16
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.79
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.64
 p-value of test no 163                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.97
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.60
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.45
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.10
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.51
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.30
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.17
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.05
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.41
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.65
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.58
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.01
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.62
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.78
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.61
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.35
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.36
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.38
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.69
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.74
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.38
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.15
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.04
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999983099
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.79
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999952709
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:47.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192217102.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27110
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.91
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.92
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.09
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.27
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.26
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.80
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.07
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.07
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.55
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.08
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.30
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.39
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.63
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.62
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.96
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.21
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908755
   j =  2                              :            45615
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908429
   j =  2                              :            45784
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.66
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.84
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.41
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.62
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.19
 p-value of test no 124                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.31
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.97
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 130                :  6.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 132                :  1.0e-2
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.64
 p-value of test no 133                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.57
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.65
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.63
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.96
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.54
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.73
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.68
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.47
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.69
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.05
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.26
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.46
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.58
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.49
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.74
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.64
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.12
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  113.37
 p-value of test no 160                :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.64
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.79
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.49
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.79
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.24
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.64
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.60
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.92
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.93
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.17
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.66
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.26
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.73
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.03
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.75
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.98
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.65
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.60
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.05
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9701.18
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.23
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.10
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.13
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.82
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12053.93
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.46
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.79
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999955529
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.41
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000025912
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:43.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193200142.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27111
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 7                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.56
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.99
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.09
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.36
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.86
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.79
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.52
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.34
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.95
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.40
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.97
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.84
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.83
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5239.93
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908208
   j =  2                              :            45893
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908262
   j =  2                              :            45866
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.49
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.01
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.31
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.61
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.47
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.81
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.41
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.03
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.71
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17061.98
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.74
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.23
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.80
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.49
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.85
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.99
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.94
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.35
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.86
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.51
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.66
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.89
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.69
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.01
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.55
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.11
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.97
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.45
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.30
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.56
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.08
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.73
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.33
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.50
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.94
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.88
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.07
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.39
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.18
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.69
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.80
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.52
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.26
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.35
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.09
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.34
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.07
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.92
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.57
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.34
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.68
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000080173
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.66
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999898520
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:13.31
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194183182.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27112
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5240
 p-value of test no 13                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    4.09
 p-value of test no 26                 :  7.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.22
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.57
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.55
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.00
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.11
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.07
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.77
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.61
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.61
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.87
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.67
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.44
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.78
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908352
   j =  2                              :            45818
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46212
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870212
   j =  1                              :        399907580
   j =  2                              :            46204
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.14
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.84
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.79
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.96
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.10
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.31
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.77
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.71
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.40
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.96
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.36
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.50
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.17
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.83
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.19
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.03
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.50
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.03
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.50
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.50
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.68
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   95.19
 p-value of test no 159                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.30
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.21
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.18
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.83
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.75
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.10
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.54
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.11
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.66
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.94
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.74
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.62
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.15
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.69
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.09
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.66
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.25
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.83
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.90
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.23
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.02
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.84
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.52
 p-value of test no 216                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.70
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.67
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.68
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.55
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.40
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.85
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.43
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999872450
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.31
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999927200
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    2.18
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:53.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195264526.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27113
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1248
 p-value of test no 6                  :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334368
   j =  1                              :        599997504
   j =  2                              :             1248
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 11                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.99
 p-value of test no 34                 :  1.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.99
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.21
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.38
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.27
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.50
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.83
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.32
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.79
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.56
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.94
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.67
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.38
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.34
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.90
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908268
   j =  2                              :            45863
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907748
   j =  2                              :            46123
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
 p-value of test no 94                 :    0.9929
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.21
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.39
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.27
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.85
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.25
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.30
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.36
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.14
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17305.36
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.68
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.51
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.85
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.03
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.90
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.62
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.62
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.09
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.19
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.76
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.68
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.83
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.02
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.16
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.76
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.97
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.43
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.35
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.81
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.94
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.46
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.63
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.10
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.16
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.88
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.36
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.93
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.80
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.91
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.67
 p-value of test no 175                :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.26
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.55
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.68
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.22
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.46
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.65
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.53
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.41
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.12
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.43
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.58
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000122854
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.64
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000050137
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    2.18
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:08.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   6  CollisionOver, t = 3            0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196280334.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27114
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.14
 p-value of test no 23                 :    0.9994    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.84
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.36
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.56
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.97
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.05
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.58
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.30
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1579.54
 p-value of test no 56                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.09
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.34
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.94
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.77
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.48
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.05
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908223
   j =  2                              :            45884
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908515
   j =  2                              :            45738
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.07
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.76
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.39
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.23
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.44
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.19
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.78
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.026
 p-value of test no 135                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.38
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.52
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.94
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.35
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.16
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.15
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.53
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.44
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.76
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.68
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.42
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.35
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.98
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.76
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.20
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.94
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.33
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.21
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.50
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.49
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.19
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.98
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.96
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.22
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.55
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.54
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.75
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.42
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.92
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.59
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 200                :  6.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 202                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.91
 p-value of test no 203                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.57
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.83
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.83
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.46
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.16
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.28
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.57
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.82
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.48
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.28
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000017650
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.55
 p-value of test no 233                :  3.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999837563
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    2.33
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:07.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197263374.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27115
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.28
 p-value of test no 28                 :  6.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    4.69
 p-value of test no 42                 :  4.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.85
 p-value of test no 46                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.65
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.05
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.61
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.48
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.67
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.75
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.23
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.61
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.45
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7301.71
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.92
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.79
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.96
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.42
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5230.53
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907963
   j =  2                              :            46011
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907911
   j =  2                              :            46043
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.72
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.43
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.83
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.29
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.05
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.47
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.07
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.29
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17715.84
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.14
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.54
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.24
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.70
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.96
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.42
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.95
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.04
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.57
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.46
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.25
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.11
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.98
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.81
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.87
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.13
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.91
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.27
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.89
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.71
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.84
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.84
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.23
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.53
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.78
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.90
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.09
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 186                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.10
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 200                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.01
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.58
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.42
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.64
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.23
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.67
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.43
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.23
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.78
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.39
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.93
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999936563
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.79
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999913415
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:53.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198475790.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27116
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.50
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.58
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.26
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.59
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.50
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.90
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.48
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.43
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.28
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.63
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.06
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.51
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908560
   j =  2                              :            45717
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907846
   j =  2                              :            46071
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 117                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.76
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.99
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.12
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.38
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.57
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.78
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.63
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.35
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.79
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.12
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17086.23
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.77
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.66
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.56
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.83
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.15
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.18
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.23
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.00
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.82
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.52
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.23
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.44
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.20
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.48
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.02
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5161.55
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.87
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.97
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.79
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.15
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.45
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.78
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.07
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.90
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.91
 p-value of test no 177                :  1.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.36
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.21
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.70
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.33
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.42
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.35
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.98
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.58
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.57
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4331.17
 p-value of test no 228                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.10
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.83
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.57
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000040942
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.03
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999965765
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 240                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:53.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199655438.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27117
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 3                  :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    4.78
 p-value of test no 36                 :  3.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     260
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.66
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.27
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.93
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.12
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.39
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.74
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.19
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6812.97
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.06
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.17
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.13
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.50
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5125.23
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908388
   j =  2                              :            45803
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908406
   j =  2                              :            45791
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.02
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.15
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.32
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.63
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.35
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.54
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.28
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.33
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.20
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.78
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17636.35
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.93
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.87
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.43
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.57
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.79
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.05
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.69
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.73
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.61
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.44
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.89
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.88
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.79
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.12
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.99
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.16
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.44
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.67
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.91
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.09
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.00
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.07
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.13
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.47
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.40
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.30
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.31
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.70
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.19
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.46
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.21
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.93
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.30
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-4
 p-value of test no 212                :    0.9990    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10400.95
 p-value of test no 215                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.33
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.09
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.04
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.71
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.39
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12080.12
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.30
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999897797
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.44
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000135610
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:29.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            8.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200671246.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27118
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 11                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.13
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.73
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.88
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.94
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.25
 p-value of test no 53                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.53
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.95
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.82
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6862.38
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.56
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.49
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.95
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.32
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908406
   j =  2                              :            45791
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46204
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870204
   j =  1                              :        399907596
   j =  2                              :            46196
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-4
 p-value of test no 109                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.54e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    5.57
 p-value of test no 111                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.75
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.51
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.68
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.25
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.53
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.13
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.80
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.21
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.68
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.39
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17604.72
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.33
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.02
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.77
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.39
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.49
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.47
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.31
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.47
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.72
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.01
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.90
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.76
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.07
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.57
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.56
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.37
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.50
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.35
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.75
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.77
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.97
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.21
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.38
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.17
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.67
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.17
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.20
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.23
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.84
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.13
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.34
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.17
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.05
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.48
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.70
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.18
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4712.50
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.52
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.70
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12100.82
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12061.18
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.80
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999859940
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.47
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000149614
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.35
 p-value of test no 243                :  9.3e-3
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:15.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201654286.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27119
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 5                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    4.14
 p-value of test no 30                 :  7.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 35                 :    0.9974
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.24
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.45
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.43
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.20
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.34
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.84
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.81
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.22
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.85
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7244.06
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.60
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.95
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.75
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5193.16
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908437
   j =  2                              :            45774
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908103
   j =  2                              :            45941
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-5
 p-value of test no 112                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 114                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.30
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.07
 p-value of test no 120                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.51
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.45
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.48
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.21
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.14
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.04
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.74
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 142                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17052.81
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.01
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.94
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.72
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.71
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.25
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.04
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.79
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.65
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.02
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.23
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.27
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.00
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.34
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.80
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.97
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.08
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.65
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.27
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.97
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.11
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.91
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.58
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.65
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.77
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.94
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.67
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.86
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.87
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.33
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.73
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.02
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 201                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.35
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.75
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.64
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.50
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.31
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.12
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.02
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4338.71
 p-value of test no 228                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11639.90
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.90
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.52
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999795644
 
 Normal statistic for number of bits   :   -1.62
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.56
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999969641
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.083
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
 p-value of test no 246                : 1 -  3.7e-5    *****
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.81
 p-value of test no 248                :    0.9975
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:16.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202670094.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27120
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 12                 :    0.9977
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4185
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.60
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.97
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.07
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.28
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.82
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.90
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.54
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.63
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.43
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.19
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7252.99
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.27
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.78
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.83
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.53
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.88
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46129
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870129
   j =  1                              :        399907744
   j =  2                              :            46125
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908327
   j =  2                              :            45829
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
 p-value of test no 76                 : 1 -  9.0e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 84                 :  1.0e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-4
 p-value of test no 103                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.50
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.06
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.89
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.63
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.79
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.51
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.41
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.86
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17297.45
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.18
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.68
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.28
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.34
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.94
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.21
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.16
 p-value of test no 155                :    0.9920
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.77
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.93
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.17
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.06
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.22
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.49
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.92
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.95
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.31
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.58
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.84
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.93
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.51
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.68
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.57
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.37
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.44
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.94
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.55
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.86
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.47
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 188                :    0.9912
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.50
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.62
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.30
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.53
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.63
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 214                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.92
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.54
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.25
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.70
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.56
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11428.93
 p-value of test no 229                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.98
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.21
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000084955
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.98
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000025939
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:31.17
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183468047.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27121
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1523
 p-value of test no 9                  :  1.3e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334643
   j =  1                              :        599996954
   j =  2                              :             1523
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.93
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.91
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.86
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.09
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.12
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.24
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.96
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.78
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.28
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.93
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.00
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.03
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.39
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908146
   j =  2                              :            45921
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908421
   j =  2                              :            45776
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.95
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.83
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.92
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.67
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.95
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.13
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.92
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.27
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.59
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.92
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.88
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.94
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.93
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.07
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.15
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.93
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.32
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.53
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.71
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.23
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.27
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.49
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.74
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.60
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.31
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.23
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.20
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.91
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.38
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.54
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.81
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.71
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.10
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.96
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.45
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.12
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.71
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.42
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.86
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.65
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.13
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.52
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.60
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.79
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.83
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.65
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.94
 p-value of test no 217                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.74
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.47
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.49
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.96
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.33
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12014.84
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.19
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000003970
 
 Normal statistic for number of bits   :   0.031
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.33
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999995813
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.42e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:01.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           1.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184582159.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27122
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9992    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.97
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.93
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.82
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.89
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.17
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.16
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.53
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.67
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.26
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.08
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908141
   j =  2                              :            45925
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.76
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.76
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.71
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.60
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.50
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.94
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.95
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.18
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.62
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.13
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.00
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.00
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.91
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.20
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.28
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.57
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.96
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.11
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.66
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.80
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.60
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.47
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.89
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.42
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.44
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.50
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.72
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.44
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.73
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.71
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.43
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.80
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.60
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.94
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.03
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.72
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.45
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.03
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.07
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.28
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.51
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.15
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.27
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.31
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.23
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.09
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.96
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.68
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.37
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.07
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.51
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.32
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.58
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000054598
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.29
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999916943
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:30.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185729039.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27123
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 7                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9908
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.83
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.45
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.80
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.67
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.17
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.65
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.50
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.66
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.91
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.67
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.22
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.70
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4918.97
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908513
   j =  2                              :            45736
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45449
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869449
   j =  1                              :        399909103
   j =  2                              :            45447
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 107                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.98
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.83
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.94
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.91
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.64
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.34
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.04
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.15
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.31
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.99
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.66
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.64
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.49
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.93
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.22
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.27
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.19
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.57
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.52
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.34
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.68
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.00
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.21
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.72
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.82
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.60
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.45
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.63
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5207.94
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.04
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.50
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.33
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.45
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.49
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.67
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.50
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.37
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.80
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.29
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.37
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.91
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.20
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.86
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.88
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.34
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.20
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.44
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.19
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.12
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999915824
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.15
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000183892
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    2.04
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:41.46
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186646543.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27124
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.59
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.44
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.82
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.66
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.71
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.90
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  350.65
 p-value of test no 55                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.92
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.90
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.76
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.70
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.64
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.65
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908051
   j =  2                              :            45961
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  7.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 104                :    0.9903
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.48
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.16
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.12
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.78
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.78
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.06
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.97
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.11
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.89
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17061.60
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.77
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.11
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.02
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.22
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.99
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.52
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.52
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.31
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.19
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.29
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.47
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.65
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.91
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.11
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.09
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.44
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.49
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.31
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.18
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.81
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.53
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.23
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.50
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.16
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.62
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.58
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 180                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 188                :  9.0e-3
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.05
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.96
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.52
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.67
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.42
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.12
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.54
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.08
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.33
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.28
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.81
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.51
 p-value of test no 231                :    0.9973
 
 
 -----------------------------------------------
 Total number of bits:  8000039493
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.16
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999812135
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:21.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187858959.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27125
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4480
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.98
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.76
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.58
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.00
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.64
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.88
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.47
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.62
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.72
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.11
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6813.44
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.66
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.81
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.50
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4892.40
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46126
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870126
   j =  1                              :        399907751
   j =  2                              :            46120
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45522
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869522
   j =  1                              :        399908956
   j =  2                              :            45522
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.33
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.89
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.43
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.82
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.94
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.83
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.61
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17765.06
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.51
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.73
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.88
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.92
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.45
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.57
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.51
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.95
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.39
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.75
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.12
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.16
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.87
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.03
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.37
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.35
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.46
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.55
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.17
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.85
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.18
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.16
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.85
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.50
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.98
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.21
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.88
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.86
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.42
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.76
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.40
 p-value of test no 207                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.01
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.94
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.77
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 224                :    0.9935
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.33
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.96
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.31
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.42
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.21
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.48
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000091027
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.71
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000020470
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:03.19
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188743695.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27126
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.05
 p-value of test no 22                 :  8.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    3.24
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.75
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.07
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.71
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.84
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.98
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.89
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.33
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.43
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.27
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.51
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.61
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.08
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.97
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.44
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.82
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.48
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45543
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869543
   j =  1                              :        399908921
   j =  2                              :            45529
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908924
   j =  2                              :            45538
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.72
 p-value of test no 118                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.35
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.08
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.01
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.94
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.54
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.48
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.22
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.28
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.11
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.82
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.88
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.23
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.19
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.35
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.69
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.07
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.15
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.58
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.73
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.69
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.26
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.28
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.02
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.84
 p-value of test no 164                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.26
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.44
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.91
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.50
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.03
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.60
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.43
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.04
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.07
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.99
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.90
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.36
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.40
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.28
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.12
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.81
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.06
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.73
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.65
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.52
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.11
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.94
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.02
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999907544
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.76
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999989111
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:49.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189661199.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27127
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.04
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.03
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.62
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.81
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.89
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.53
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.77
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.05
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.76
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.30
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.22
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.54
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.51
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908168
   j =  2                              :            45910
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907887
   j =  2                              :            46052
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-3
 p-value of test no 100                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
 p-value of test no 104                :    0.9955
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.24
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.14
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.33
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.25
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.28
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.19
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.73
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.07
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.46
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.33
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17728.00
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.08
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.11
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.97
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.88
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.50
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.55
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.38
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.00
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.01
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.54
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.81
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.47
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.54
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.68
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.21
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.00
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.32
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.41
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.62
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.35
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5244.30
 p-value of test no 168                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.54
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.93
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.58
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.39
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.15
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.36
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.70
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.86
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.87
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.67
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.89
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.87
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.55
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.57
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.64
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.49
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.45
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.04
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.32
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.19
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999928211
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.16
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000118216
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.28
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:26.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191004687.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27128
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.33
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    3.79
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.75
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.84
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.48
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.61
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.89
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.82
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.89
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.17
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.64
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.90
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.24
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.83
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5197.84
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908748
   j =  2                              :            45620
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908031
   j =  2                              :            45977
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.48
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.97
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.41
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.01
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.58
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.49
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.68
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.50
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.72
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.03
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.15
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17644.25
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.90
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.81
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.82
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.13
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.73
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.77
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.80
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.12
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.09
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.51
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.33
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.10
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.56
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.18
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.73
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.29
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.56
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.50
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.84
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.18
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.18
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.35
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.92
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  443.21
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.06
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.09
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.87
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.62
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.71
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.53
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.37
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.75
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.88
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.32
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.60
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.16
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.95
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11587.56
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.14
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999945950
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.12
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999823865
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:22.84
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191987727.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27129
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 3                  :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 10                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.19
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.36
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.11
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.20
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.58
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.03
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.27
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.98
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.57
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.95
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.51
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.09
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.01
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.10
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.26
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907606
   j =  2                              :            46191
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45456
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869456
   j =  1                              :        399909092
   j =  2                              :            45448
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-4
 p-value of test no 113                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    6.49
 p-value of test no 114                :  5.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.91
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.86
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.89
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.68
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.87
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.84
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.55
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.31
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.82
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.69
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.14
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.84
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.29
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.63
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.68
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.57
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.22
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.45
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.43
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.26
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.02
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.46
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.17
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.17
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.02
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.59
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.13
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.36
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.26
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.66
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.00
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.75
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.97
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.24
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.04
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.18
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.45
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.98
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.83
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.51
 p-value of test no 177                :    0.9940
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.06
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.36
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.88
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 201                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.03
 p-value of test no 203                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.88
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.17
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.03
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.21
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.00
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.93
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.26
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12185.67
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.75
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.28
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999991631
 
 Normal statistic for number of bits   :  -0.066
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.61
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999870320
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.60
 p-value of test no 253                :    0.9954
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:25.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  54  SampleMean, r = 10              5.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192937999.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27130
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1496
 p-value of test no 10                 :  2.3e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334616
   j =  1                              :        599997008
   j =  2                              :             1496
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.89
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.99
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.74
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.90
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.78
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.40
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.24
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.46
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.54
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.99
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.18
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.49
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.22
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.41
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907801
   j =  2                              :            46095
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.31
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.34
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.33
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.10
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.41
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.31
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.44
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.25
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.94
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.14
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.68
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.78
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.89
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.70
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.32
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.05
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.58
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.29
 p-value of test no 156                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.27
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  407.47
 p-value of test no 158                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.55
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.09
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.41
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.83
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.54
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.00
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.31
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.41
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.93
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.75
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.10
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.65
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.29
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.14
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.74
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.91
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.98
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.50
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.99
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.04
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.25
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 204                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.21
 p-value of test no 207                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9781.39
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.29
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.70
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.88
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.10
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.34
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.76
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.58
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.00
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999995888
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.94
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000034510
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.95
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:22.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           2.3e-4
  76  RandomWalk1 J (L=1000, r=0)     0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194019343.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27131
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.05
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.35
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.12
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.80
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.51
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.69
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.47
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.30
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.93
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.48
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.30
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.02
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.51
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46111
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870111
   j =  1                              :        399907781
   j =  2                              :            46105
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46210
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870210
   j =  1                              :        399907582
   j =  2                              :            46206
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.05
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.24
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.08
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.88
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.59
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.12
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.60
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.27
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.81
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.63
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.50
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.55
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.18
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.81
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.53
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.82
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.74
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.80
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.45
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.04
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.08
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.75
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.11
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.42
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.27
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.65
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.28
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.11
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.17
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.01
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.94
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.43
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.56
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.99
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.34
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.00
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.45
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.26
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.51
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.81
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.12
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.03
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.51
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.71
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4476.82
 p-value of test no 228                :  5.6e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.73
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.25
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000019396
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.22
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999727190
 
 Normal statistic for number of bits   :   -2.16
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.100
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 250                :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  98  HammingIndep, L=300, r=26       5.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195035151.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27132
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 11                 :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5272
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 19                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.09
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.96
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.99
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.43
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.61
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.09
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.15
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.17
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.97
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.44
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.38
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 64                 :    0.9995    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.68
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.82
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.41
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5239.17
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908521
   j =  2                              :            45735
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908576
   j =  2                              :            45703
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.84
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.83
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.37
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.35
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.69
 p-value of test no 123                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.24
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.80
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.76
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.13
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.76
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 142                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    5.47
 p-value of test no 144                :  1.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18047.25
 p-value of test no 145                :  5.4e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.70
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.87
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.89
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.00
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.82
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.46
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.43
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.27
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.11
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.17
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.64
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.35
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.45
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.49
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.33
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.09
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.48
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.49
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.70
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.12
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.85
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.89
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.54
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.40
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.26
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.98
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.30
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.25
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.03
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.81
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.54
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 209                :    0.9915
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9708.30
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.98
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.11
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-4
 p-value of test no 224                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4697.29
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.07
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.87
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11471.85
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12178.90
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.35
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999924794
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.87
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000044821
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 252                :  9.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 253                :  7.9e-3
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:39.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  73  GCD                             5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196050959.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27133
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    4.33
 p-value of test no 32                 :  6.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.15
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.65
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.21
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.08
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.11
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.35
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.08
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.27
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.28
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.97
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.96
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.24
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5171.24
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45409
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869409
   j =  1                              :        399909185
   j =  2                              :            45403
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.74
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.23
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.71
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   15.73
 p-value of test no 124                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.99
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.91
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.62
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.93
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17186.98
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.00
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.78
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.09
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.74
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.60
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.82
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.35
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.24
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.40
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.38
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.18
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.50
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.63
 p-value of test no 160                :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.44
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.06
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.23
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.42
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.08
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.43
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.46
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.53
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.09
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.44
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.94
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.85
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.76
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.95
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.98
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.08
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.03
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.86
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.88
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.56
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.11
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.14
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.45
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.79
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.87
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.20
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000015928
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.74
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000211129
 
 Normal statistic for number of bits   :    1.67
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:47.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  64  WeightDistrib, r = 26           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197001231.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27134
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    4.48
 p-value of test no 44                 :  5.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.91
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.63
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.52
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.94
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.35
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.05
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.73
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7253.08
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.50
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.04
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.35
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.85
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45528
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869528
   j =  1                              :        399908947
   j =  2                              :            45522
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908358
   j =  2                              :            45818
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.77
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.57
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.38
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.39
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.49
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.28
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.67
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.82
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17379.09
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.73
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.10
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.33
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.31
 p-value of test no 149                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.74
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.28
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.35
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.42
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.98
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.30
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.14
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.10
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.12
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.66
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.77
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.86
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.31
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.33
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.21
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.08
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.56
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.26
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.57
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.53
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.73
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.31
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.04
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.65
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.26
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 192                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.86
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.23
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.74
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.50
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.19
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.63
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.52
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.56
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.13
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.19
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.73
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.06
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999965021
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.21
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999860468
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:53.85
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197951503.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27135
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1244
 p-value of test no 12                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334364
   j =  1                              :        599997512
   j =  2                              :             1244
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    3.43
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     348
 p-value of test no 37                 :  3.6e-3
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.42
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.12
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.70
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.65
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.63
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.00
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.72
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.43
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.44
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.10
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.33
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.52
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.76
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907853
   j =  2                              :            46057
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908140
   j =  2                              :            45930
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 76                 :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
 p-value of test no 90                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.16
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.09
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.60
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.13
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.90
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.51
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.77
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.75
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.72
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17384.78
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.00
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.56
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.61
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.11
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.71
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.43
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.63
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.30
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.47
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.70
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.02
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.03
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.85
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.74
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.40
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.45
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.75
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.37
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.47
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.38
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.19
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.55
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.60
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.58
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.31
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.12
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.94
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.71
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.98
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.06
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.91
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.76
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.78
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.06
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.02
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.20
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.40
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.27
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.28
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.59
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.22
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.04
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.47
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.49
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.40
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000006880
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.15
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999948968
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 238                :    0.95
 
 Sample variance                       :    2.26
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:07.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198967311.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27136
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 11                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.12
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.32
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.75
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.25
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.45
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.73
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.09
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.07
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.22
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.30
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.36
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.52
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.15
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908465
   j =  2                              :            45766
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46018
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870018
   j =  1                              :        399907966
   j =  2                              :            46014
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 87                 :    0.9915
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 91                 :    0.9919
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.28
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.83
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.88
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.21
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.75
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.53
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.86
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.32
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.77
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.60
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.62
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.46
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.61
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.10
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.24
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.98
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.21
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.12
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.44
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.91
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.60
 p-value of test no 156                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.56
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.01
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.97
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.01
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  209.20
 p-value of test no 161                :  4.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.73
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.57
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.88
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.88
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.90
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.20
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.01
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.31
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.74
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.17
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.27
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.46
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.74
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.10
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.75
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.82
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.77
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.96
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.52
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.90
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.64
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.17
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.23
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.50
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.64
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.17
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.37
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.34
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.12
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.85
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999984815
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.71
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000102064
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:30.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199950351.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27137
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4130
 p-value of test no 16                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9908
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.64
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.95
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.25
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.84
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.10
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.31
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.14
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.35
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.99
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.10
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.29
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.45
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.31
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.00
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46286
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870286
   j =  1                              :        399907431
   j =  2                              :            46280
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907609
   j =  2                              :            46185
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.40
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.72
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.54
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.68
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.45
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.69
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.81
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 143                :    0.9960
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17089.19
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.58
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.86
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.95
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.97
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.58
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.16
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.50
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.26
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.01
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.90
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.97
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.54
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.01
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.89
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.08
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.88
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.37
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.09
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.62
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.83
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.75
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.32
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.39
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.12
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.05
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.84
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.43
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.41
 p-value of test no 196                :    0.9942
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.60
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.32
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.64
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.62
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.11
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.65
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4738.26
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.03
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.33
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.03
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.85
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999976814
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.53
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999827930
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:14.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200900623.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27138
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.51
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.67
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.20
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.91
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.55
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.56
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.22
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.51
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6887.61
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.55
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.90
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.80
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.84
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.59
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907608
   j =  2                              :            46184
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908279
   j =  2                              :            45853
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 97                 :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.81
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.61
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.38
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.26
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.25
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.01
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.36
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.41
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.62
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.37
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.06
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.92
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.71
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.06
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.68
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.10
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.97
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.37
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.72
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.36
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.52
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.50
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.65
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.07
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.67
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.79
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.21
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.20
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.02
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.31
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.57
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.69
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.94
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.17
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.02
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.90
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.15
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.04
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.18
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.80
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.00
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.72
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.47
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.02
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.70
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.95
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.88
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.44
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4287.40
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.78
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.71
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.06
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000028444
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.96
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000106918
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9943
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:57.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201916431.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27139
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.84
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.58
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.73
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.36
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.35
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.91
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.23
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.56
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.08
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.50
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.92
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.52
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45475
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869475
   j =  1                              :        399909051
   j =  2                              :            45473
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908547
   j =  2                              :            45722
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 80                 :    0.9905
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.15
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.70
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.58
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.32
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.73
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.29
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.62
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.83
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.94
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17839.57
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.93
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.00
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.17
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.06
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.96
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.82
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.33
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.81
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.63
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.40
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.10
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.39
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.99
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.33
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.23
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.91
 p-value of test no 163                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.65
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.56
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.60
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.19
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.59
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.35
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.07
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.62
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.39
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.89
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.88
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.88
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.59
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.27
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.26
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.92
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.46
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.80
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.73
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.42
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.77
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.56
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.73
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.54
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.50
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999819632
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.78
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000078469
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:23.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202866703.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27140
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 9                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7551
 p-value of test no 19                 :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    4.25
 p-value of test no 36                 :  6.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.16
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.90
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     183
 p-value of test no 43                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.30
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.28
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.61
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.03
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.83
 p-value of test no 51                 :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.35
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.76
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.96
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.19
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.18
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.82
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.46
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.96
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.47
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.87
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46309
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870309
   j =  1                              :        399907388
   j =  2                              :            46297
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908308
   j =  2                              :            45840
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.22
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.74
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.41
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.92
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.60
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.46
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.84
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.13
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.16
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.42
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.31
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.53
 p-value of test no 146                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.41
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.28
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.54
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.69
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.79
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.10
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.18
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.42
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.86
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.68
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.95
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.11
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.22
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   99.21
 p-value of test no 161                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.58
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.32
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.16
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.97
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.60
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.36
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.37
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.12
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.92
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.82
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.46
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.06
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.55
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.97
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.81
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.42
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.21
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.09
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.68
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.86
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.24
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.37
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.44
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.62
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.36
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999955916
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.69
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000000985
 
 Normal statistic for number of bits   : 7.79e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:55.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183500816.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27141
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.97
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.70
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.07
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.23
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.77
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.89
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.07
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.77
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6747.21
 p-value of test no 57                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.99
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.56
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.87
 p-value of test no 66                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.86
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5232.48
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908601
   j =  2                              :            45692
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908568
   j =  2                              :            45710
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.58
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.33
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.39
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.48
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.46
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.66
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.77
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.66
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.78
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.73
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.08
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.17
 p-value of test no 149                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.69
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.48
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.55
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.87
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.21
 p-value of test no 154                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.14
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.67
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.33
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.85
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.38
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.16
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.15
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.89
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.44
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.13
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.28
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.08
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.78
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.67
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.87
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.07
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.30
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.93
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.13
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.64
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.83
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.15
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.04
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.40
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.76
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.04
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.77
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.59
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.70
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.09
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.85
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.20
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000018811
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.65
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000046948
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:32.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184287248.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27142
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 12                 :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7546
 p-value of test no 15                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.87
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.63
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.84
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.97
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.96
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.26
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.86
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.41
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.91
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.98
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.77
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.97
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.67
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907857
   j =  2                              :            46070
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908446
   j =  2                              :            45768
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.67
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.93
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.59
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.63
 p-value of test no 122                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.92
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.28
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.96
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.82
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.46
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.50
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17796.19
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.56
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.49
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.18
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.78
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.84
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.62
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.99
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.67
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.83
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.87
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.02
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.70
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.17
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.63
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.75
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.49
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.19
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.71
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.64
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.67
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.99
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.27
 p-value of test no 172                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.56
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.98
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.24
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 185                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    5.54
 p-value of test no 187                :  1.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.25
 p-value of test no 188                :  5.8e-4    *****
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.80
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.70
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.63
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.23
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.07
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.99
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.43
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.22
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.88
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.43
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.31
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.27
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000065485
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.26
 p-value of test no 233                :  4.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999903545
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:21.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               5.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185106448.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27143
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 12                 :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9978
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    3.44
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    3.32
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.59
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.89
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.03
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.62
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.76
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.11
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.42
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.81
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.14
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.95
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.17
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.33
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.09
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5209.07
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908479
   j =  2                              :            45759
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907975
   j =  2                              :            46005
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.80
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.28
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.76
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.25
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.61
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.44
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.05
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.37
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.11
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.84
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.34
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.34
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.58
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.48
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.79
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.82
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.82
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.23
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.33
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.15
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.74
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.67
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.33
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.51
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.50
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.67
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.18
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.26
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.31
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.47
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.18
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.70
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.36
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.68
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.41
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.82
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.18
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.17
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.10
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.53
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.37
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.26
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.37
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.09
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.40
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.23
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.46
 p-value of test no 216                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.77
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.45
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.95
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.92
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.49
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.99
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.69
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000027760
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.85
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000018451
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:14.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186122256.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27144
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 8                  :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.44
 p-value of test no 23                 :  1.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    3.51
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.81
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.51
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.01
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.98
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.59
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.96
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.22
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.84
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.87
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6768.27
 p-value of test no 57                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.73
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.94
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.67
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.66
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907834
   j =  2                              :            46074
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46165
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870165
   j =  1                              :        399907670
   j =  2                              :            46165
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.99
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.73
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.41
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.43
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.95
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.79
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.43
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.40
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   92.81
 p-value of test no 141                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17531.85
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.18
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.53
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.09
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.52
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.70
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.92
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.05
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.57
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.82
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.89
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.67
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.90
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.79
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.98
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.27
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.98
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.29
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.57
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.01
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.98
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.25
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.08
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.30
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.71
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.72
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.35
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.85
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 186                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.53
 p-value of test no 188                :  5.8e-3
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.80
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.67
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.89
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.87
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.31
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.02
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.86
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.09
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.78
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.14
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.17
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999816905
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.76
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999984980
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:20.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7            4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187138064.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27145
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4186
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.91
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.03
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.68
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.03
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.56
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.32
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.69
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.06
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.89
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.02
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.68
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.38
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.87
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.31
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.76
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.52
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46434
 p-value of test no 70                 :  4.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870434
   j =  1                              :        399907135
   j =  2                              :            46428
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907742
   j =  2                              :            46123
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.80
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.51
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.23
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.98
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.66
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.02
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.96
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 143                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17079.34
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.90
 p-value of test no 146                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.95
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.49
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.17
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.65
 p-value of test no 150                :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.14
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.67
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.96
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.71
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.39
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.19
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.84
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.91
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.95
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.69
 p-value of test no 163                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.79
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.58
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.81
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.77
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.69
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.76
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.58
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.57
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.44
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.41
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.32
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.54
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.39
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    2.31
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.95
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.44
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.37
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.91
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.42
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.65
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.44
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.88
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.86
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.68
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.46
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.86
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000006664
 
 Normal statistic for number of bits   :   0.053
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.24
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999974510
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:25.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188317712.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
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                     Run no 27146
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.70
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.38
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.73
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.49
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.67
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.97
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.90
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.68
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1592.84
 p-value of test no 56                 :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.75
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.63
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.64
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.51
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.06
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908093
   j =  2                              :            45952
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908394
   j =  2                              :            45800
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 95                 :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  3.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-4
 p-value of test no 112                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.22
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.38
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.39
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.59
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.06
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.57
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.41
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.82
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.12
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.41
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.05
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.83
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.55
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.54
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.23
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.46
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.03
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.72
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.98
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.33
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.02
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.43
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.93
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.05
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.46
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.51
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.62
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.54
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.45
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.98
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4727.83
 p-value of test no 168                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.19
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.16
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.69
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.49
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.62
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.25
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.69
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.99
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.72
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.08
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.33
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.90
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.65
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.34
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.72
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.40
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.82
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.75
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.72
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000180934
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.32
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999956366
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9965
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.60e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.52
 p-value of test no 253                :    0.9941
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:13.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189857808.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27147
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.47
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.28
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.15
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.53
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.67
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.08
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.78
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.84
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.21
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.30
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.16
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.45
 p-value of test no 66                 :    0.9940
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.54
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.12
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908493
   j =  2                              :            45749
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907622
   j =  2                              :            46189
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
 p-value of test no 79                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 106                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.51
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.37
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.31
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.76
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.52
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.96
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.53
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.93
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17254.76
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.71
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.10
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.28
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.28
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.84
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.26
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.32
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.16
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.22
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.90
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.93
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.69
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.85
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.49
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  203.84
 p-value of test no 161                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.63
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.67
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.75
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.69
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.46
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.67
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.84
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.50
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.54
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.36
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.66
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.67
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.73
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.46
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.46
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.24
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.29
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.26
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.15
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.69
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.32
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.55
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 216                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 218                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.66
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.83
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.97
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.04
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.27
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.24
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.00
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999904793
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.54
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999940172
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    2.04
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:45.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190742544.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27148
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.72
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.75
 p-value of test no 47                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.15
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.69
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.14
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.62
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.05
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.85
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.17
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6899.86
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.63
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.53
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.52
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.31
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.94
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46277
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870277
   j =  1                              :        399907450
   j =  2                              :            46269
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908168
   j =  2                              :            45913
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-4
 p-value of test no 104                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.74
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.93
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.51
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.66
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.62
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.52
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.03
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.59
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.94
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.56
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.64
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.64
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.69
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.65
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.81
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.36
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.47
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.07
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.81
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.54
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.96
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.73
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.31
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.43
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.56
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.38
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.88
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.79
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.51
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.43
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.07
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.30
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.92
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.86
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.37
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.20
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.85
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.93
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.77
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.67
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.89
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.97
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.87
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.48
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3970.45
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.66
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.20
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.06
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.06
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999898499
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.44
 p-value of test no 233                :    0.9912
 
 
 -----------------------------------------------
 Total number of bits:  7999920903
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:49.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191725584.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27149
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997253
   j =  2                              :             1372
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997293
   j =  2                              :             1352
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    5.71
 p-value of test no 36                 :  1.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     359
 p-value of test no 37                 :  5.1e-4    *****
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.17
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.69
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.62
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.47
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.80
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.99
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.49
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.36
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.28
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.25
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.01
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.94
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.91
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.45
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908311
   j =  2                              :            45840
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907776
   j =  2                              :            46112
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.78
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.21
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.64
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.39
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.91
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.32
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.81
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   70.75
 p-value of test no 129                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.57
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.096
 p-value of test no 134                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.45
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.63
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.75
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.90
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.24
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.94
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.27
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.00
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.16
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.31
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.40
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.27
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.77
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.07
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.45
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.21
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.80
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.46
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.15
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.32
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.46
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.45
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.50
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.27
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.36
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.34
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.48
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.08
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.79
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.94
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    1.61
 p-value of test no 178                :    0.9998    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.85
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.75
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.25
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.47
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.80
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.14
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.49
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.65
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.11
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.75
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.46
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.37
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000021085
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.28
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000113992
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    2.15
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NJumps, t = 9        5.1e-4
  81  LinearComp, r = 0               0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192675856.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27150
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5579
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.41
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.01
 p-value of test no 28                 :  8.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.41
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.40
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.82
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.36
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.70
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.33
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.11
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.15
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.62
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.04
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.04
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.11
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.22
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.45
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.70
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4919.92
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908142
   j =  2                              :            45923
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907920
   j =  2                              :            46034
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.63
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.84
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.05
 p-value of test no 122                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.63
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.43
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.56
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.83
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.47
 p-value of test no 137                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.29
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17401.06
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.55
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.03
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.19
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.27
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.38
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.62
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.07
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.68
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.92
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.29
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.11
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.36
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.51
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.26
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.00
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.77
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.33
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.00
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.39
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.92
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.55
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.32
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.26
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.70
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.98
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.07
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.19
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.57
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.60
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.96
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.43
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.28
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    2.28
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.67
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.32
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.02
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.25
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.45
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.76
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5116.82
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.54
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.71
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.83
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.43
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.11
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000009487
 
 Normal statistic for number of bits   :   0.075
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.99
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999890840
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 250                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 251                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.44
 p-value of test no 253                :  7.4e-3
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193658896.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27151
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     539
 p-value of test no 31                 :    0.9939
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.88
 p-value of test no 39                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.13
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.70
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.22
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.06
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.37
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.59
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.69
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.75
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.49
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.54
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7198.44
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.46
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.72
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.27
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.54
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.40
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908268
   j =  2                              :            45863
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908054
   j =  2                              :            45967
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-3
 p-value of test no 86                 :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  9.1e-3
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 88                 :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.86
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.32
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.74
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.90
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.07
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.01
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.31
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.16
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.77
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.97
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 142                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 144                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16922.32
 p-value of test no 145                :    0.9970
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.52
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.22
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.02
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.61
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.89
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.88
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.64
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.84
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.67
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.03
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.07
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.03
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.58
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.93
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.71
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.57
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.45
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.52
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.09
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.66
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.76
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.24
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.11
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.46
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.64
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.84
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 185                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.70
 p-value of test no 188                :  3.5e-3
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.62
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.70
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.79
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.88
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.08
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.64
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.47
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.01
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.08
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.01
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.20
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.17
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000102583
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999998909
 
 Normal statistic for number of bits   : -8.63e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:36.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194609168.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27152
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7536
 p-value of test no 15                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 44                 :    0.9985
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.47
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.44
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.84
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.06
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.69
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.14
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.52
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.75
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.50
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.98
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.91
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.80
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.62
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.90
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.45
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.03
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.05
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908134
   j =  2                              :            45927
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46266
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870266
   j =  1                              :        399907469
   j =  2                              :            46264
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.41
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.60
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.24
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.96
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.10
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.84
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.63
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.29
 p-value of test no 135                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.17
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.02
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.44
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.21
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.05
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.00
 p-value of test no 149                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.43
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.08
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.41
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.11
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.68
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.92
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.03
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.47
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.68
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.15
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.27
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.95
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.58
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.94
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.44
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.68
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.04
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.92
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  462.74
 p-value of test no 171                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.83
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.73
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.48
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.09
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.04
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.06
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.79
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.17
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 210                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9614.08
 p-value of test no 211                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.64
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4711.65
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.80
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.33
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.93
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.58
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.94
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.21
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000049204
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.70
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999956915
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.019
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 251                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:22.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195592208.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27153
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.80
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.18
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.03
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.65
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.96
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.03
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.53
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.65
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.09
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.43
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.31
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.10
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.37
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4878.52
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908571
   j =  2                              :            45710
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908103
   j =  2                              :            45944
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.80
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.27
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.06
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.72
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.81
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.20
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.38
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.72
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.73
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17292.57
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.49
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.30
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.32
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.92
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.44
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.73
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.93
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.06
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.00
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.35
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.21
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.08
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.82
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.97
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.72
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.39
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.92
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.28
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.09
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.47
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.72
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.95
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.47
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.07
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.37
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.95
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.23
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.54
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.33
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10270.83
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.13
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.47
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.26
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.47
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.46
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.11
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11383.46
 p-value of test no 230                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.50
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000019375
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.24
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999954113
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    2.01
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.07
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:42.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196476944.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27154
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 34                 :    0.9976
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.20
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.23
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.06
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.43
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.38
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.80
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.85
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.79
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.55
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.93
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.06
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908507
   j =  2                              :            45739
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908397
   j =  2                              :            45797
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.28
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.07
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.59
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.06
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.13
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.57
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.61
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.77
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.93
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.43
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.42
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.15
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.26
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.82
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.44
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.25
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.98
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.91
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.04
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.91
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.77
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  422.87
 p-value of test no 158                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.64
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.63
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.04
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.26
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.08
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.90
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.80
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.33
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.66
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.20
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.32
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.98
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.78
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.11
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.19
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.86
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.26
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.93
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.12
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.46
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.88
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.13
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.78
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5103.61
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.67
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.33
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.96
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.90
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.62
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000078025
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.38
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000035077
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:05.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197427216.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27155
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    3.74
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.81
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.40
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.26
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.31
 p-value of test no 51                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  178.48
 p-value of test no 54                 :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.47
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.21
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.24
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 58                 :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.32
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.79
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.93
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.49
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.16
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908452
   j =  2                              :            45765
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908226
   j =  2                              :            45881
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.45
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.37
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.60
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.91
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.97
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.95
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.06
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.57
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 139                :    0.9923
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.90
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.35
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.45
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.38
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.79
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.10
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.64
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.84
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.64
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.00
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.88
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.73
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.22
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.86
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.77
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.09
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.60
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.35
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.61
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.86
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.12
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.24
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.55
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.35
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.55
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.76
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.67
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.40
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.82
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.11
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  145.00
 p-value of test no 175                :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.63
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.28
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.76
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.97
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.15
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.05
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.41
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -3.94e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.86
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.17
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.45
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.13
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.37
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.92
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.85
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999872318
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999956258
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 246                :    0.9925
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:32.60
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198443028.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27156
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.11
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.80
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.21
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.84
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.90
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.38
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.44
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.48
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.85
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.11
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.68
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.55
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.73
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.73
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908684
   j =  2                              :            45655
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908088
   j =  2                              :            45950
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.80
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.59
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.77
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.01
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.52
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.09
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.44
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.56
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17218.64
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.65
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.17
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.71
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.67
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.23
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.02
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.58
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.49
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.24
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.22
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.14
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.53
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.57
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.98
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.04
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.50
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.42
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.08
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.17
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.58
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.98
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.42
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.83
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.37
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.01
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.23
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.79
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.93
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.91
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.36
 p-value of test no 203                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.91
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.07
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.85
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.63
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.15
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.94
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.04
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.55
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11501.19
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.13
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999988862
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.36
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000030415
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 241                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 242                :  5.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.74
 p-value of test no 243                :  3.0e-3
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:29.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199557140.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27157
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7497
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 22                 :    0.9967
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.69
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.53
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.26
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.13
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.93
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.27
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.69
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.00
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7212.87
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.44
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.26
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.18
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  163.75
 p-value of test no 67                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.29
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908167
   j =  2                              :            45912
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907872
   j =  2                              :            46058
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.83
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.18
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.94
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.75
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.72
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.15
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.01
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.54
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.19
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-3
 p-value of test no 139                :    0.9987
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   98.98
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.82
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.05
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.69
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.50
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.24
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.09
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.80
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.33
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.20
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.19
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.04
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.01
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.61
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.00
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.53
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.39
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.91
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.21
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.59
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.24
 p-value of test no 167                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.97
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.72
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.77
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.77
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.66
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.59
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.37
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.48
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.85
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.71
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.79
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.15
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 208                :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9667.87
 p-value of test no 211                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.06
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.20
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4683.15
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.49
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.03
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12057.89
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12013.36
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.84
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000047497
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.45
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999899258
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.22
 p-value of test no 244                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:32.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200605716.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27158
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 8                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.59
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.96
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   26.11
 p-value of test no 50                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.10
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.83
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.50
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.15
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.93
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.66
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.38
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.38
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.20
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.32
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908484
   j =  2                              :            45749
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907999
   j =  2                              :            45996
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 77                 :    0.9908
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.72
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.43
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.16
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.82
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.84
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.73
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.52
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.79
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.75
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.33
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.47
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.11
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.94
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.83
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.80
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.57
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.32
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.01
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.37
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.87
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.17
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.42
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.09
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.41
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.35
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.99
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.58
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.68
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.92
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.55
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.24
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.83
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.90
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4797.65
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.18
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.41
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.90
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.72
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.61
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.77
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.86
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.18
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.13
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.71
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.76
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.73
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.31
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.72
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999997550
 
 Normal statistic for number of bits   :  -0.019
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.22
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999999413
 
 Normal statistic for number of bits   : -4.64e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.90
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:22.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201588756.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27159
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 5                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 28                 :    0.9962
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     549
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.47
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.82
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.72
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.90
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.49
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.94
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.90
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.38
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.65
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.66
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.91
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.60
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.77
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.03
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46140
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907728
   j =  2                              :            46124
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908265
   j =  2                              :            45860
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
 p-value of test no 94                 :    0.9943
 
 Anderson-Darling statistic = A2       :    5.48
 p-value of test no 95                 :  1.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9995    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.64
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.75
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.48
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.95
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.94
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.93
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.50
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.80
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.85
 p-value of test no 135                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.58
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.71
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.20
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.53
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.16
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.55
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.52
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.61
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.97
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.08
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.39
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.09
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.73
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.79
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.52
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.10
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.97
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.38
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.02
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.29
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.29
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.41
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.22
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.88
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.01
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.68
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.47
 p-value of test no 172                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.18
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.78
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.89
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.00
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.04
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.51
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10240.93
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.06
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.15
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.85
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.49
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.23
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.47
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.36
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000165643
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.16
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000156349
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    4.95
 p-value of test no 237                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.77
 p-value of test no 238                :    0.9972
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 241                :    0.9934
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 243                :    0.9910
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:00.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202571796.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27160
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.16
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.82
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.34
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.22
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.58
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.46
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.30
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.21
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6889.68
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.61
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 63                 :  2.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.95
 p-value of test no 64                 :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.16
 p-value of test no 65                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.36
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.89
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.16
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45542
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908918
   j =  2                              :            45538
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907664
   j =  2                              :            46165
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-4
 p-value of test no 112                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.36
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.97
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.49
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.25
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.39
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.16
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.33
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.78
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.38
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.67
 p-value of test no 136                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.96
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.94
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17706.49
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.83
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.67
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.97
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.96
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.08
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.74
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.70
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.53
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.00
 p-value of test no 155                :    0.9932
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.25
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.00
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.40
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.85
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.94
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.10
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.23
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.57
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.71
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.26
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.08
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.74
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.33
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.40
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.50
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.67
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.89
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.07
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.58
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.09
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 185                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.17
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.14
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.03
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.73
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.34
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9692.33
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.47e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.19
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.80
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.48
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.51
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.68
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.19
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.17
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999796841
 
 Normal statistic for number of bits   :   -1.61
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.01
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000074614
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:03.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183533585.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27161
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7553
 p-value of test no 15                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.58
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.52
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.51
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.08
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.58
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.41
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.98
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.19
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.56
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.45
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.28
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.55
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.34
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908719
   j =  2                              :            45633
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45391
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869391
   j =  1                              :        399909220
   j =  2                              :            45387
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 97                 :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.36
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.53
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.97
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.89
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.45
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.47
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.87
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.94
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.69
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.20
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17266.59
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.37
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.75
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.38
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.55
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.50
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.09
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.27
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.80
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.68
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.24
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.69
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.91
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.40
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.48
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.27
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.20
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.83
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.88
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.04
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.51
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.65
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.89
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.40
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.96
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.68
 p-value of test no 171                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.29
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.27
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.89
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.71
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.00
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.31
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.65
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.25
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.92
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.48
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.40
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.45
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.75
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.09
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.77
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.19
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.27
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999928727
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.17
 p-value of test no 233                :    0.9921
 
 
 -----------------------------------------------
 Total number of bits:  8000131236
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.077
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:51.60
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184385553.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27162
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1245
 p-value of test no 8                  :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334365
   j =  1                              :        599997510
   j =  2                              :             1245
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9935
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.53
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.32
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.77
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.49
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.68
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.57
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.51
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.71
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 58                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.80
 p-value of test no 59                 :  3.2e-4    *****
 
 Anderson-Darling statistic = A2       :    8.66
 p-value of test no 60                 :  6.6e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   67.80
 p-value of test no 61                 :  9.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.05
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.64
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.70
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46219
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907563
   j =  2                              :            46217
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907828
   j =  2                              :            46074
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 78                 : 1 -  4.9e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-5
 p-value of test no 110                :    0.9939
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 111                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.50
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.74
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.95
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.87
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.88
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.48
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.62
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.96
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.28
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17449.50
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.40
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.23
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.91
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.83
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.63
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.05
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.25
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.20
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.12
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.40
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.11
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.69
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.75
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.42
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.18
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.60
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.23
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.12
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.60
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.27
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.53
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.44
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.91
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.61
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.28
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.24
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.57
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.88
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.34
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.56
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.91
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.00
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.12
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.08
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.01
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.88
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.02
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.53
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.06
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.42
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.63
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.64
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.13
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12162.19
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.10
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000078661
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.81
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999973889
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 253                :    0.05
 
 Sample variance                       :    2.12
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:29.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7            0.9994 
  38  Run, r = 0                      9.5e-5
  46  MaxOft AD, t = 8               1 -  4.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185466897.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27163
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 8                  :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.70
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.69
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.43
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.59
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.24
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.21
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.69
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.65
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.26
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1564.00
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.75
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.63
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.89
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.47
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4876.14
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907966
   j =  2                              :            46017
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907667
   j =  2                              :            46162
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 77                 :    0.9953
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 91                 :    0.9903
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.38
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.13
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.80
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.49
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.13
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.01
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.31
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.79
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17495.87
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.06
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.82
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.41
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.61
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.04
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.19
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.63
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.09
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.29
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.33
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.26
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.18
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.06
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.42
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.85
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.89
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.18
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.29
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.88
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.24
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.44
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.50
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.19
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.36
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.88
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.38
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.28
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.18
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.02
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.42
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.07
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.51
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.08
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.56
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.77
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.27
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.78
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.18
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12033.03
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.44
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000143179
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.26
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000004303
 
 Normal statistic for number of bits   :   0.034
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:35.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186548241.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27164
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 8                  :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1485
 p-value of test no 12                 :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.47
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.86
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.73
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.73
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.93
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.39
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.15
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.55
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.36
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.35
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.64
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.91
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.14
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.97
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.73
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908322
   j =  2                              :            45830
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908754
   j =  2                              :            45617
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.043
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.84
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.52
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.06
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.67
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.67
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.58
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.60
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.11
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.00
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.06
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.00
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.18
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.82
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.22
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.23
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.82
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.19
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.81
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.19
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.80
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.56
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.42
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.81
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.92
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.23
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.90
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.64
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.48
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.85
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.44
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.00
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.92
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.49
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.50
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.72
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.04
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.50
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.08
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.64
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.27
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.51
 p-value of test no 179                :    0.9940
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.32
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.38
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.63
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.98
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.80
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.91
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.31
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.32
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.39
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.80
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.72
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.15
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999821828
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.73
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999835454
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:31.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187596817.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27165
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 8                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    3.48
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.97
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.70
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.94
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.51
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.38
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.59
 p-value of test no 53                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.59
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.28
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.73
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.39
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.99
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.20
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.05
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.87
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45533
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869533
   j =  1                              :        399908937
   j =  2                              :            45527
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908263
   j =  2                              :            45861
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 83                 :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.04e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.90
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.10
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.28
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.90
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.57
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.86
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.03
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.75
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.65
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.74
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.30
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.11
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.02
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.28
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.73
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.06
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.32
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.06
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.34
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.64
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.47
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.95
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.70
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.88
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.67
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.63
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.16
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.78
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.05
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.35
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.65
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.63
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.13
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.84
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.20
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.05
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.12
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.80
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.82
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.13
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.84
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.80
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.47
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.64
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.36
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.83
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12165.12
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.41
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.92
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999908441
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.54
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000059698
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.064
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:29.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188579857.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27166
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 10                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.26
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9903
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.61
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.13
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.98
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.57
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.82
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.63
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.25
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.55
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.09
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.42
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.08
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.16
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.00
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.43
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.55
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908716
   j =  2                              :            45636
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907941
   j =  2                              :            46025
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.85e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.80
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.99
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.60
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.44
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.59
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.54
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.36
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.28
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.35
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 138                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 139                :  3.5e-4    *****
 
 Anderson-Darling statistic = A2       :    9.03
 p-value of test no 140                :  4.2e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  216.05
 p-value of test no 141                :  3.2e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.39
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.84
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.48
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.31
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.38
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.23
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.59
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.70
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.64
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.70
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.35
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.38
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.42
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.53
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.40
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.29
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.47
 p-value of test no 166                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.18
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5192.71
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.55
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.60
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.18
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.18
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.98
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.62
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.34
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.78
 p-value of test no 176                :  5.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.44
 p-value of test no 177                :    0.9927
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.08
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.16
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.18
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.73
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.67
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.87
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.59
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4697.69
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.53
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.96
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.70
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.51
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.84
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999964325
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.66
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000194410
 
 Normal statistic for number of bits   :    1.54
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.14e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:27.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          3.2e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189923345.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27167
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 11                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    3.27
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.87
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.02
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.03
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.37
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.89
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.78
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.66
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.52
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6945.06
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.54
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.15
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.36
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.83
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4834.83
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907822
   j =  2                              :            46086
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46263
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870263
   j =  1                              :        399907475
   j =  2                              :            46261
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 86                 :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.81
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.08
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.87
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.75
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.84
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.86
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.93
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.23
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 143                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 144                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17832.60
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.97
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.23
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.58
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.07
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.47
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.24
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.01
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.08
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.10
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.56
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.80
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.44
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.22
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.85
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.68
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.32
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.72
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.09
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.10
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.15
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.01
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.64
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.10
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.99
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.99
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.33
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.17
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.73
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.07
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.23
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.72
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.05
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.39
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.90
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.30
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.87
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.20
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3961.55
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.75
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11539.51
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.81
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.48
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000113479
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.78
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999853100
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:20.35
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190775313.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27168
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.23
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.06
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.12
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.84
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.63
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.97
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.84
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.08
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.76
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.07
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.83
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.90
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907761
   j =  2                              :            46118
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908006
   j =  2                              :            45988
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.84
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.05
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.82
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.44
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.39
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.85
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.41
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.96
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.76
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.46
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.70
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.78
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.46
 p-value of test no 149                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.50
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.75
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.14
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.75
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.78
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.60
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.62
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.33
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.56
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.44
 p-value of test no 161                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.26
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.55
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.11
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.65
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.11
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.64
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.70
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.11
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.22
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.22
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.10
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.43
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.85
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.04
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.29
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.13
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.22
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.04
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.32
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.13
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.23
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 219                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5098.74
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.92
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.13
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.69
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.04
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12112.52
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.32
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999976967
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.72
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000207319
 
 Normal statistic for number of bits   :    1.64
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:08.19
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191758353.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27169
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7555
 p-value of test no 20                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.13
 p-value of test no 29                 :  7.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.82
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.45
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.71
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.57
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.27
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.87
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.82
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.74
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.23
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.04
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.28
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.88
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.62
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.07
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.36
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908242
   j =  2                              :            45870
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908124
   j =  2                              :            45926
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-4
 p-value of test no 113                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.23
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.61
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.63
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.02
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.53
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.14
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.10
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.90
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.85
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.093
 p-value of test no 134                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.61
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17747.08
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.84
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.25
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.80
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.89
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.93
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.80
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.59
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.86
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.88
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.12
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.23
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.84
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.27
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.75
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.04
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.97
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.39
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.25
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.64
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.19
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.50
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.77
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.13
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.19
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.36
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.37
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.87
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.32
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.41
 p-value of test no 178                :  1.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.21
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.20
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.76
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.43
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 213                :  1.0e-3
 
 Anderson-Darling statistic = A2       :    5.27
 p-value of test no 214                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10409.41
 p-value of test no 215                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.09
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.46
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.20
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.50
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.93
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.29
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.41
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999990758
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.95
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999941264
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:12.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192708625.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27170
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.01
 p-value of test no 47                 :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.31
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.17
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.19
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.99
 p-value of test no 51                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.74
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.14
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.13
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.63
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.44
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.24
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.10
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.94
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.06
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.44
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907814
   j =  2                              :            46087
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908009
   j =  2                              :            45991
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.92
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.43
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.68
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.96
 p-value of test no 122                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.18
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.73
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.89
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.02
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17248.90
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.09
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.11
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.46
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.93
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.79
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.32
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.09
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.19
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.23
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.29
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.95
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.43
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.54
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  591.53
 p-value of test no 163                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.10
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.87
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.61
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.54
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.32
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.41
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.39
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.48
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.91
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.91
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.83
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.91
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.30
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.45
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.90
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.26
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.79
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.75
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.56
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.18
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.17
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.15
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.36
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.31
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000091330
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000029383
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:19.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193691665.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27171
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    3.58
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.45
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.20
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.38
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.87
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.54
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.76
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.76
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.71
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7219.99
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.96
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.21
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.44
 p-value of test no 66                 :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.24
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5211.44
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907916
   j =  2                              :            46036
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908496
   j =  2                              :            45749
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
 p-value of test no 106                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.22
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.44
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.05
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.33
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.17
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.80
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.44
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.47
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.07
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.06
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.04
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.52
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.56
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.41
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.82
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.86
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.92
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.52
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.36
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.50
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.86
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.73
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.46
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.54
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.60
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.15
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.67
 p-value of test no 167                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.04
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.87
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.31
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.23
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.08
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.21
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.20
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.79
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.49
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.15
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.28
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 206                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  253.15
 p-value of test no 207                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 210                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9643.00
 p-value of test no 211                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.71
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.95
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.75
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.63
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4329.83
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.39
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.62
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.82
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000015382
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.39
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000005308
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:36.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194674705.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27172
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.84
 p-value of test no 41                 :  1.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.06
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.30
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.43
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.93
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.95
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.84
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.13
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.48
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.85
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.01
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.53
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.18
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.72
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.91
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5197.30
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45656
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869656
   j =  1                              :        399908693
   j =  2                              :            45646
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46251
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870251
   j =  1                              :        399907498
   j =  2                              :            46251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 101                :    0.9953
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.82
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.53
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.11
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.82
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.46
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.22
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.66
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 131                :  2.4e-4    *****
 
 Anderson-Darling statistic = A2       :    7.71
 p-value of test no 132                :  1.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   76.37
 p-value of test no 133                :  4.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.63
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.71
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.99
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.46
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.07
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.96
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.66
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.42
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.35
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.23
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.74
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.45
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.27
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.36
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.28
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.66
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.28
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.81
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.95
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.21
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.24
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.55
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.41
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.10
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.09
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.39
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.67
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.59
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.13
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.02
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.54
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.22
 p-value of test no 196                :    0.9964
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.67
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.56
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.83
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.29
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.15
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.21
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.13
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.52
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.56
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.13
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.95
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.18
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000061396
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.74
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000048523
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.083
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:58.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195788817.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27173
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 10                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1504
 p-value of test no 12                 :  1.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334624
   j =  1                              :        599996992
   j =  2                              :             1504
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5219
 p-value of test no 13                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9953
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.65
 p-value of test no 46                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.70
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.07
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.30
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.20
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.19
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.53
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.39
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.51
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.14
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.24
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.37
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.25
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45569
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908864
   j =  2                              :            45565
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908212
   j =  2                              :            45894
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.14
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.99
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.63
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.44
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.54
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.30
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.40
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 143                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17843.04
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.67
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.96
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.74
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.23
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.40
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.33
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.79
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.15
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.91
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.05
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.00
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.98
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.35
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.67
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.63
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.48
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.76
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.77
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.95
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.57
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.26
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.19
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.43
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.89
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.09
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.55
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.03
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.59
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.82
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.69
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.92
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.67
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.91
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.27
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.74
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11494.24
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.97
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.29
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000195478
 
 Normal statistic for number of bits   :    1.55
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.25
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000000520
 
 Normal statistic for number of bits   : 4.11e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 1.20e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:51.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196771857.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27174
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.09
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.16
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.08
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.21
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.90
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.50
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.81
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.37
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.81
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.91
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.36
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.99
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.42
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.04
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45526
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908950
   j =  2                              :            45522
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908322
   j =  2                              :            45830
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.89
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.25
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.04
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.27
 p-value of test no 122                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.58
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.36
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.45
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.06
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.36
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.98
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.80
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.95
 p-value of test no 147                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.32
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.68
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.66
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.97
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.66
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.08
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.69
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.72
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.81
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.91
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.12
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.07
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.60
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.64
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.02
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.26
 p-value of test no 166                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.68
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.73
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.08
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.31
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.41
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.54
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.04
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.73
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.41
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    2.09
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.42
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.12
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.76
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.44
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.80
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.62
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.19
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.78
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.25
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.44
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.36
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.30
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999871352
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.90
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999887555
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:17.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197787665.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27175
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9926
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.61
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.24
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.58
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.49
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.21
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.04
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.45
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.42
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.93
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.40
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908456
   j =  2                              :            45766
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908512
   j =  2                              :            45741
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.88
 p-value of test no 119                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.82
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.88
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.32
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.56
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.04
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.44
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.31
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.60
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.76
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.69
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.92
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.42
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.45
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.37
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.83
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.29
 p-value of test no 153                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.32
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.15
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.92
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.45
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.42
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.64
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.97
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.42
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.19
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.90
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.16
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.95
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.21
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.17
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.81
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.88
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.97
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.81
 p-value of test no 171                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.19
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.01
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.24
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.52
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.17
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.81
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.28
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.91
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.13
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.21
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.57
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.07
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.29
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.95
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11579.99
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.71
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.99
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999850961
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.14
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999967511
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 247                :    0.9990    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:00.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198737937.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27176
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.56
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.37
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.71
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.58
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.63
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.20
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.78
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.40
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.41
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.08
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.12
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.77
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.74
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.48
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.51
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.91
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908579
   j =  2                              :            45706
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908412
   j =  2                              :            45791
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.14
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.18
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.82
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.00
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.25
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.34
 p-value of test no 125                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.45
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.93
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.32
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17762.46
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.20
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.21
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.82
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.67
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.80
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.89
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.46
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.76
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.10
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.30
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.36
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.21
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.23
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.99
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.65
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.44
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.55
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.32
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.15
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.68
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.91
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.16
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.10
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.32
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.21
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.60
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.14
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.01
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.25
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.40
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.17
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.29
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.40
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.16
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.60
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.04
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12055.10
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.91
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000172243
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.74
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999953006
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:36.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199688209.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27177
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.33
 p-value of test no 34                 :  2.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.01
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.02
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.28
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.41
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.36
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.13
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.54
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.73
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.51
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.71
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.33
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.07
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.77
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.93
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.03
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.79
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908671
   j =  2                              :            45660
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907898
   j =  2                              :            46045
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.43
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.75
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.77
 p-value of test no 123                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.46
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.23
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.45
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17192.70
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.16
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.74
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.11
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.48
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.60
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.28
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.74
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.99
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.25
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.24
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.48
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.25
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.08
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.36
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.58
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.24
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.68
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.19
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.07
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4754.49
 p-value of test no 168                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.93
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.45
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.59
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.38
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.59
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.95
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.15
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.30
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.01
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.04
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.74
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.30
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.23
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.11
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.43
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.16
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4347.70
 p-value of test no 227                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.76
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.94
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.58
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.80
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999921053
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.07
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000160330
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200998929.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27178
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.18
 p-value of test no 35                 :  2.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    7.13
 p-value of test no 38                 :  3.0e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    3.29
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.03
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.44
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.48
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.24
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.29
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.98
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.21
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.11
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.83
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.88
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.55
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.89
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908033
   j =  2                              :            45979
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-4
 p-value of test no 113                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.44
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.32
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.16
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.97
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.04
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.35
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.68
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17293.02
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.22
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.96
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.44
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.64
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.21
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.41
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.68
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.80
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.04
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.77
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.85
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.32
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.27
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.53
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.57
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.87
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.49
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.32
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.33
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.01
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.12
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.12
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.94
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.39
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.38
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.65
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.85
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.16
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.35
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 209                :    0.9930
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 210                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9573.83
 p-value of test no 211                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.25
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.31
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.22
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.07
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.88
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.27
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.36
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.04
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999987014
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.13
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999977675
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    2.25
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.24
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:58.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201981969.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27179
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    4.75
 p-value of test no 39                 :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.43
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.93
 p-value of test no 49                 :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.17
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.13
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.70
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.87
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.97
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6894.95
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.71
 p-value of test no 59                 :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 60                 :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.89
 p-value of test no 61                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.98
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.02
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.32
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908310
   j =  2                              :            45842
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45555
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869555
   j =  1                              :        399908894
   j =  2                              :            45547
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-4
 p-value of test no 112                :  7.7e-6    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    6.73
 p-value of test no 114                :  4.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.86
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.54
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.89
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.81
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.54
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.43
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.32
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.64
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.98
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17658.78
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.75
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.87
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.00
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.31
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.40
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.20
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.00
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.21
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.26
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.10
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.59
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.33
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.73
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.10
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.26
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.96
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.07
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.28
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.72
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.39
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.72
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.35
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.12
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.23
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.71
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.66
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.09
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.91
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.67
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.79
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   27.38
 p-value of test no 198                :  6.1e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.43
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.91
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.46
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.69
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.07
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.34
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.01
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.31
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.13
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.88
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.18
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999965624
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.62
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000009361
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:58:22.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  54  SampleMean, r = 10              4.5e-4
  87  LongestHeadRun, r = 27          6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202932241.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27180
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.26
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.80
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.43
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.13
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.10
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.22
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.15
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.58
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.04
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.02
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.56
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.10
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5214.65
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908271
   j =  2                              :            45863
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908323
   j =  2                              :            45831
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 101                :    0.9939
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 111                : 1 -  5.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.16
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.06
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.06
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.98
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.75
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.78
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.13
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.34
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.02
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.72
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.74
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.35
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.00
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.04
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.36
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.32
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.46
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.52
 p-value of test no 156                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.33
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.97
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.16
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.31
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.61
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.00
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.08
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.22
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.15
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.62
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.21
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.76
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.25
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.37
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.15
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.51
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.94
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.00
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.40
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.30
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.07
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.44
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.23
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.25
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.38
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.47
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.11
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.10
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.08
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.06
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.47
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000057649
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.51
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999962870
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 243                :    0.96
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:22.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  53  SampleMean, r = 0              1 -  5.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183566354.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27181
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 5                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 11                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5574
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    3.18
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.99
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.22
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.90
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.25
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.61
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.84
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.76
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.76
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.12
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.67
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.20
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 63                 :  4.1e-3
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 64                 :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.68
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.13
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.95
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.09
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45394
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869394
   j =  1                              :        399909216
   j =  2                              :            45386
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908708
   j =  2                              :            45640
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.16
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.86
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.69
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.58
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.45
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.27
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.83
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.62
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.08
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.00
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.99
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.81
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.34
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.46
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.00
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.08
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.24
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.06
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.37
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.55
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.60
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.24
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.10
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.74
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.28
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.28
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.69
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.56
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.06
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.94
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.91
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.14
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.02
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.49
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.43
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.92
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.16
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.52
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.04
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.57
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.12
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.98
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   31.97
 p-value of test no 198                :  9.4e-5    *****
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.29
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.65
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.74
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.90
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 216                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.27
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.27
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.63
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.63
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.21
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.78
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.47
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000013189
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999882587
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 243                :    0.47
 
 Sample variance                       :    2.04
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:59.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  87  LongestHeadRun, r = 27          9.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184057874.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27182
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4540
 p-value of test no 17                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    6.70
 p-value of test no 44                 :  4.7e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.08
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.29
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.10
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.23
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.01
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.67
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.65
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.40
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.56
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.97
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.68
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.27
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  162.09
 p-value of test no 67                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.68
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 : 1 -  6.2e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46194
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870194
   j =  1                              :        399907613
   j =  2                              :            46192
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908400
   j =  2                              :            45794
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.34
 p-value of test no 117                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.81
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.52
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.65
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.84
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.01
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.72
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.96
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17059.27
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.74
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.11
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.69
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.02
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.31
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.81
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.29
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.88
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.86
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.92
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.27
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.43
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.09
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.62
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.27
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.42
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.37
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.05
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.40
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.43
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.86
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.57
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.75
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.75
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.67
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.60
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.96
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.37
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.28
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.11
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.49
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.42
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.90
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.49
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.52
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 220                :    0.9929
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4663.94
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.10
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.02
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.80
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.05
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.17
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.18
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999980657
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.91
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000058372
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.093
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.64
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
 p-value of test no 245                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 248                :  7.0e-3
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 250                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:52.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         4.7e-4
  43  Permutation, t = 10            1 -  6.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185008146.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27183
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.94
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.39
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.33
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.38
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.00
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.26
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.63
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.69
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.26
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.24
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.03
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.45
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.63
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907966
   j =  2                              :            46011
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908397
   j =  2                              :            45794
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.54
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.28
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.79
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.48
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.25
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.67
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 138                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 140                :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   95.80
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17703.11
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.26
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.74
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.30
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.01
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.22
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.42
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.74
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.61
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.25
 p-value of test no 156                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.40
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.97
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.40
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.13
 p-value of test no 160                :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.02
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.95
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.26
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.66
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.04
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.51
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.57
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.79
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.95
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.97
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.60
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.95
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.20
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.99
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.96
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.76
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.46
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 185                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.85
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.48
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.20
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.22
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.37
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 223                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.35
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4307.95
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.49
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.44
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.59
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.77
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000032500
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.22
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999971768
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:30.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186023954.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27184
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5590
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.79
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.53
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.44
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.01
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.52
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.35
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.45
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.63
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.05
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6887.02
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.76
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.69
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.95
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.59
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908592
   j =  2                              :            45695
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908356
   j =  2                              :            45819
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.51
 p-value of test no 116                :  2.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.22
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.28
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.56
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.75
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.63
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.16
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.07
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.78
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.05
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.76
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17235.89
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.68
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.85
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.84
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.18
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.96
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.89
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.30
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.77
 p-value of test no 153                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.46
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.63
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.50
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.79
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.48
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.74
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.62
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.67
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  189.60
 p-value of test no 164                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.00
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.70
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.12
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.77
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.62
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.63
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.74
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.12
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.61
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.63
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.21
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.63
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-4
 p-value of test no 186                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.49
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.40
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10157.79
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10268.20
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.55
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.26
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.64
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.82
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.82
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.60
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.60
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999944063
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.11
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999878840
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:15.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               2.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187039762.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27185
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5615
 p-value of test no 13                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.65
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     121
 p-value of test no 43                 :    0.9916
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.22
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.97
 p-value of test no 49                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.43
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.33
 p-value of test no 51                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.66
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.01
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.32
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.62
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.52
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.65
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 58                 :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.90
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 63                 :  2.9e-3
 
 Anderson-Darling statistic = A2       :    6.65
 p-value of test no 64                 :  5.3e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  101.51
 p-value of test no 65                 :  6.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.45
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.27
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5161.67
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908585
   j =  2                              :            45700
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908530
   j =  2                              :            45729
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 111                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.51
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.98
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.50
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.53
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.60
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.56
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.70
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.61
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.42
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.52
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.37
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.02
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.21
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.63
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.29
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.23
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.38
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.27
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.06
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.86
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.14
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.44
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.59
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.51
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.79
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.84
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.77
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.99
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.72
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.55
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.45
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.40
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.33
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.76
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.67
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.94
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.40
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.88
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.31
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.22
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.39
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.48
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.66
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.41
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.01
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10266.58
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.81
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 219                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.98
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
 p-value of test no 223                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5104.22
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.69
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.22
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.94
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.65
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.55
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999950723
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.37
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000045550
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188350482.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27186
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 3                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    3.17
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.21
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.50
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.38
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.42
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.41
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.69
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.53
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.07
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6826.06
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.52
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.19
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.29
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5270.39
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  4.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908362
   j =  2                              :            45813
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907892
   j =  2                              :            46048
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.37
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.97
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.43
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.61
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.16
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.32
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.66
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.53
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.07
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.91
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.64
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.12
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.31
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.73
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.55
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.87
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.69
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.19
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.52
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.71
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.38
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.00
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.18
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.00
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.65
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.19
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.80
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.02
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.63
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.06
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.72
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.98
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.10
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.12
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.93
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 182                :  9.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 183                :    0.01
 
 Sample variance                       :    2.32
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.13
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.00
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.18
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.51
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10231.05
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.39
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.66
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.63
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.24
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.43
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.43
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.14
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000031930
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999908609
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:33.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            0.9990 
  43  Permutation, t = 10             4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189235218.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27187
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4531
 p-value of test no 17                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.07
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.45
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.98
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.58
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.18
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.83
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.38
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.37
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.59
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.67
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.83
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.08
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.67
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.19
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.75
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908068
   j =  2                              :            45963
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908459
   j =  2                              :            45766
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.45
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.41
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.36
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.44
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.67
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.15
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.10
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.62
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.68
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.05
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 143                :    0.9913
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16966.47
 p-value of test no 145                :    0.9938
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.06
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.63
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.19
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.65
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.60
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.73
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.47
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.82
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.20
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.90
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.40
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.42
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.65
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.09
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.92
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.39
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.58
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.94
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.44
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.55
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.41
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.13
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.95
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.45
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.53
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.04
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.98
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.26
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.24
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.96
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.34
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.47
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.78
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.38
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.20
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.76
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.20
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.61
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.47
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.33
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11559.92
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.50
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000015568
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.62
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999941144
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:38.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190251026.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27188
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 19                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.42
 p-value of test no 41                 :  6.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.09
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.24
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.49
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.50
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.20
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.40
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.14
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.65
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.48
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.79
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.19
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.99
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.99
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.86
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.02
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907795
   j =  2                              :            46098
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908637
   j =  2                              :            45680
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 91                 :    0.9916
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 92                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.58
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.40
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.53
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.08
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.33
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.26
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.45
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.26
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.97
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.67
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.58
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.01
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.67
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.64
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.34
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.97
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.70
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.74
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.79
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.92
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.17
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.56
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.03
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.51
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.32
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.99
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.49
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.56
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.94
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.70
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.42
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.59
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.46
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.38
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.85
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.07
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.84
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.32
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.47
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.16
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.04
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.07
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9760.76
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.21
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.59
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.23
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.82
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.33
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.72
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.53
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000020356
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.79
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000066877
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 250                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:00.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191266834.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27189
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5273
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4488
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.52
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.05
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.06
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.74
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.33
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.67
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.93
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.62
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.93
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.54
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.58
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.79
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908472
   j =  2                              :            45758
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908587
   j =  2                              :            45699
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.90
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.37
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.78
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.26
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.19
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.51
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.96
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.30
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.74
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.91
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.75
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.77
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.76
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.92
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.58
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.66
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.28
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.98
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.41
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.00
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.01
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.23
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.71
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.50
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.02
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.87
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.99
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.03
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.01
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.85
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.99
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.13
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.50
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.92
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.93
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.47
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.16
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.27
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.28
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.45
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.30
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.91
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.46
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.72
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.18
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.84
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11601.78
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.44
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999759734
 
 Normal statistic for number of bits   :   -1.90
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.26
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000060847
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 251                :  9.7e-4    *****
 
 Anderson-Darling statistic = A2       :    6.41
 p-value of test no 252                :  6.8e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.04
 p-value of test no 253                :  1.2e-3
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:03.86
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192249874.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27190
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1492
 p-value of test no 8                  :  3.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334612
   j =  1                              :        599997016
   j =  2                              :             1492
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   24.40
 p-value of test no 47                 :  9.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.55
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.18
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.67
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.57
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.43
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.35
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.36
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.76
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.04
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.87
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.95
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.18
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.25
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.95
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.49
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46308
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870308
   j =  1                              :        399907386
   j =  2                              :            46304
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45633
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869633
   j =  1                              :        399908737
   j =  2                              :            45627
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.83
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.75
 p-value of test no 122                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.27
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.61
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.25
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.07
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.30
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.70
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.36
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.29
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.71
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.15
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.39
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.81
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.72
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.28
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.78
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.70
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.17
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.85
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.22
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.29
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.88
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.43
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.90
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.14
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.07
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.04
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.76
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.99
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.05
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.11
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.69
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.81
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.17
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5231.06
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.42
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.81
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.82
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.93
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 200                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    7.49
 p-value of test no 202                :  2.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  135.85
 p-value of test no 203                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.90
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10259.31
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.94
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.84
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.66
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.26
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.36
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.47
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.40
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.84
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999952421
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.82
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999778166
 
 Normal statistic for number of bits   :   -1.75
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:16.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7            3.4e-4
  27  SimpPoker, r = 27               9.7e-4
  88  PeriodsInStrings, r = 0         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193265682.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27191
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 3                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5566
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    5.09
 p-value of test no 27                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.44
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.80
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.97
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.84
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.33
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.66
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.63
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.28
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.47
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.47
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.35
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.05
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.36
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.66
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908387
   j =  2                              :            45802
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908044
   j =  2                              :            45975
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.32
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.53
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.97
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.86
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.19
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.08
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
 p-value of test no 139                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.14
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17579.88
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.31
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.90
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.19
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.41
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.14
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.21
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.86
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.51
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.47
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.73
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.83
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.42
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.46
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.57
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.62
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.75
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.75
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.96
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.88
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.62
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.29
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.40
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.66
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  299.40
 p-value of test no 174                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.54
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.59
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.25
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.02
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.39
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.66
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.00
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.25
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.63
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.32
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.97
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4293.30
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.92
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.87
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.03
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000013681
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000060790
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.041
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.82e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194215954.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27192
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 38                 :    0.9966
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.70
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.42
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.56
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.55
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.21
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.56
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.36
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.76
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.14
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.82
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.64
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.91
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.05
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.34
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.86
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.40
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908235
   j =  2                              :            45878
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908110
   j =  2                              :            45936
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
 p-value of test no 80                 :    0.9967
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.03
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.86
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.25
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.13
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.73
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.37
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.91
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.67
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17647.29
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.34
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.49
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.73
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.60
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.89
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.91
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.41
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.95
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.82
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.28
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.54
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.33
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.97
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.03
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.02
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.88
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.11
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.83
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.12
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.57
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5246.67
 p-value of test no 168                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.71
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.81
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.41
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.22
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.15
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.99
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.30
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.37
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.52
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9929
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.62
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.85
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.39
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.76
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.86
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.10
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.49
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.24
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.93
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.66
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.72
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000097543
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.08
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000062107
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:22.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195198994.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27193
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.52
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.72
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.90
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.79
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.23
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.42
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.81
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.43
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.12
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.69
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.47
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.91
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45642
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908720
   j =  2                              :            45634
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46036
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907930
   j =  2                              :            46032
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.92
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.00
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.16
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.16
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.27
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.26
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.56
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.35
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.53
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.71
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
 p-value of test no 143                :    0.9948
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17211.61
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.39
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.89
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.27
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.97
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.07
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.83
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.86
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.75
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.31
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.27
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.03
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.26
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.32
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.73
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.32
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.81
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.44
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.17
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.41
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.33
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.43
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.57
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.25
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.26
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.62
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.46
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.05
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.24
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.42
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.66
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.19
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.88
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.15
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.82
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.23
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.25
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.26
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.75
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.66
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.61
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999896801
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.56
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000028372
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    2.31
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:09.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196247570.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27194
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 12                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7588
 p-value of test no 15                 :  8.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.65
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.10
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.85
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.92
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.18
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1539.85
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.24
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.73
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.40
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.23
 p-value of test no 66                 :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.56
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.76
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908150
   j =  2                              :            45922
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908249
   j =  2                              :            45874
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 106                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.35e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.30
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.80
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.25
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.42
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.43
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.67
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.39
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9978
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.13
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.12
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17178.23
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.20
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.58
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.75
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.39
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.52
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.23
 p-value of test no 152                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.25
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.63
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.11
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.65
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.13
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.98
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.27
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.46
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.83
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.07
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.43
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.45
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.30
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.84
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.34
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.21
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.38
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.58
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.90
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.73
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.40
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.29
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.88
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.43
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.86
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.48
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.19
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.27
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.22
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4304.49
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.45
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.72
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.44
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.60
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999960161
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.24
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000056512
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:18.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         8.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197230610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27195
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9968
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    4.21
 p-value of test no 39                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.79
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.76
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.46
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.14
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.69
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.31
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6875.82
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.93
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.37
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.11
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.63
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908394
   j =  2                              :            45797
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46264
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870264
   j =  1                              :        399907477
   j =  2                              :            46254
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 101                :    0.9942
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 102                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 115                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.90
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.40
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.99
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.25
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.00
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.39
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.05
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.36
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.75
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17190.15
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.03
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.82
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.21
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.66
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.16
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.16
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.73
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.97
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.15
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.41
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.06
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.19
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.33
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.76
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.69
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.69
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.19
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.25
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.61
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.68
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.75
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.13
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.20
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.93
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.58
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.80
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.57
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.34
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.71
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.08
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.87
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.98
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.05
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.37
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.99
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.92
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.52
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.31
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.46
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.46
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.70
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.19
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.33
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000032377
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.42
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999941171
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198246418.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27196
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.63
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.17
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.26
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.56
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.64
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.57
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.85
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7355.84
 p-value of test no 57                 :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.02
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.40
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.13
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.21
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.15
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908420
   j =  2                              :            45787
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45465
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869465
   j =  1                              :        399909075
   j =  2                              :            45455
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.10
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.13
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.08
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.21
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.82
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.48
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.61
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.30
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.54
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.55
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17255.51
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.45
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.17
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.56
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.90
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.71
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.87
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.50
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.83
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.93
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.09
 p-value of test no 157                :  2.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.55
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.45
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.33
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.02
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.85
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.94
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.24
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.35
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.69
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.24
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4822.70
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.25
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.05
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.64
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.17
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.07
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.97
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.79
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.95
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.85
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.26
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.04
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.00
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.11
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.65
 p-value of test no 218                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.10
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4677.28
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.05
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.22
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.63
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.05
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.20
 p-value of test no 231                :    0.9945
 
 
 -----------------------------------------------
 Total number of bits:  8000010096
 
 Normal statistic for number of bits   :   0.080
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.08
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999895268
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:22.48
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199262226.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27197
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 10                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.97
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.62
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.61
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.91
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.28
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1358.62
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.61
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.37
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.92
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.10
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.64
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908189
   j =  2                              :            45898
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45519
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908970
   j =  2                              :            45503
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-5
 p-value of test no 112                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.23
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.19
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.28
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.53
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.68
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.13
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.12
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.79
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.13
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.69
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17683.59
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.48
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.25
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.24
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.70
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.45
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.82
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.29
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.00
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.32
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.83
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.97
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.72
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.53
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.77
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.42
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.28
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.45
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.10
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.80
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.55
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.93
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4808.77
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.98
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.59
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.80
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.40
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.35
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.43
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.45
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.81
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.33
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.54
 p-value of test no 179                :  5.6e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.98
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.89
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.26
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.49
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.63
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.30
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.72
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.91
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.56
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.83
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.67
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.78
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999936341
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.97
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000003016
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.034
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:19.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200245266.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27198
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     966
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.23
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.35
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.69
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.10
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.43
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.51
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.45
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.99
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.36
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.50
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 62                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.58
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.20
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.35
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.29
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46096
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907815
   j =  2                              :            46082
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907992
   j =  2                              :            46001
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.08
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.32
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.31
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.10
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.01
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.59
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.34
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.99
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.78
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.01
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.53
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.50
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.08
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.01
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.20
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.90
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.97
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.66
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.15
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.50
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.90
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.24
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.81
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.14
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.97
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.34
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.52
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.17
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.11
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.19
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.98
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.34
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.39
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.28
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.46
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.14
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.18
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.77
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
 p-value of test no 180                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.44
 p-value of test no 183                :  7.3e-3
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.43
 p-value of test no 188                :  7.6e-3
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.47
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.27
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.21
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.87
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.59
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.55
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 216                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.13
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.23
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.75
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.59
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.48
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.10
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.20
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000098413
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.48
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000037096
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 247                :  8.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.62
 p-value of test no 248                :  4.5e-3
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:18.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201326610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27199
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.47
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.44
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.11
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.75
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.92
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.19
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.53
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.63
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.15
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.68
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.41
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.82
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.70
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4905.66
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45496
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869496
   j =  1                              :        399909014
   j =  2                              :            45484
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908457
   j =  2                              :            45770
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 81                 :    0.9976
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 85                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.22
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.89
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.44
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.02
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.16
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.75
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.96
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.63
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.58
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.28
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.27
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17155.23
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.49
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.14
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.48
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.27
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.42
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.73
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.73
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.03
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.74
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.66
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.44
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.68
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.69
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.91
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.19
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.37
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.24
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.94
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.91
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.80
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.40
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.67
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.19
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.36
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.35
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.86
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.53
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.51
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.96
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.23
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.96
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.28
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9739.34
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
 p-value of test no 220                :    0.9977
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.16
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.35
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.54
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.99
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.64
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.83
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.52
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999857015
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000090295
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.15
 p-value of test no 239                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:06.80
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202276882.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27200
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 8                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.86
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.69
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.46
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.72
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.60
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.20
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.90
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.23
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7302.24
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.66
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 64                 :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   95.80
 p-value of test no 65                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.16
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.34
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.77
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908345
   j =  2                              :            45820
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908054
   j =  2                              :            45970
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.78
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.30
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.46
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.28
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.24
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.44
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.44
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.92
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.26
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.62
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.98
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.33
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.88
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.89
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.86
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.22
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.87
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.88
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.53
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.15
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.24
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.13
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.51
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.08
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.28
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.28
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.91
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.64
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.30
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.29
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.88
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.65
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.38
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.93
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.37
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.65
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.46
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.97
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.63
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.27
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.91
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.28
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.92
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.28
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.28
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.78
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.99
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.25
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.93
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.63
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.59
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.29
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999955679
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.96
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999860429
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:20:28.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183599123.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27201
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 12                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.48
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.75
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.31
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.38
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.28
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.76
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.51
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.17
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.92
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.48
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.27
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.50
 p-value of test no 66                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.28
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.95
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908663
   j =  2                              :            45664
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908115
   j =  2                              :            45932
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.41
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.83
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.08
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.78
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.40
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.16
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.16
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.20
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17890.01
 p-value of test no 145                :  7.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.19
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.09
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.97
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.28
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.31
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.84
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.44
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.88
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.17
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.39
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.52
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.84
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.32
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.53
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.86
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.20
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.30
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.24
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.20
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.43
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.52
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.71
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.30
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.41
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.55
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.94
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.77
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.56
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.57
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.08
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.95
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.41
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.58
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10233.40
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.09
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.64
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.27
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.73
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.83
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.11
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.75
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999981809
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.72
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999932600
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:23.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184942611.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27202
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 4                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.54
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.40
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.36
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.47
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.49
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.64
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.71
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.87
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.54
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.73
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.91
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5203.08
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907933
   j =  2                              :            46029
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908345
   j =  2                              :            45817
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.29
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.43
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.94
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.02
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.20
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.52
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.35
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.33
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.36
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.89
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.11
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.12
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.41
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.09
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.74
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.18
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.82
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.43
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.57
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.97
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.18
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.43
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.44
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.11
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.88
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.22
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.13
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.37
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.50
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.64
 p-value of test no 166                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.96
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.59
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  258.70
 p-value of test no 170                :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.76
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.75
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.30
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.51
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.89
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.35
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 193                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 195                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.72
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.82
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.22
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.76
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.98
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.21
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.95
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.30
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.40
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.20
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.05
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.73
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999912263
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.71
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999962108
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.24
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:03.81
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185991187.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27203
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5250
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    3.42
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.04
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.96
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.75
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.85
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.42
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.30
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.55
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7319.57
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.56
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.97
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.05
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.45
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.81
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908198
   j =  2                              :            45895
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45981
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908043
   j =  2                              :            45971
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 81                 :    0.9981
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.93
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.51
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.93
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.75
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.15
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.42
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.78
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 130                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.08
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.85
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.62
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17733.22
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.76
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.00
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.62
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.77
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.03
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.24
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.12
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.49
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.14
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.55
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.97
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.34
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.61
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.23
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.67
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.31
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.24
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.73
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.64
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.85
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.99
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.95
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.58
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.08
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.83
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  472.05
 p-value of test no 171                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.35
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.68
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.82
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.88
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.36
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.08
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.05
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.28
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.48
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 204                :  3.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 206                :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.23
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.44
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.46
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.12
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.37
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.93
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.71
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.88
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.12
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.73
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000050938
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.23
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999856007
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:11.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186974227.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27204
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7519
 p-value of test no 21                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 30                 :    0.9971
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.79
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.84
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.42
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.56
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.77
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.54
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.29
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.67
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.46
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.43
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.12
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.63
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.61
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.37
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908437
   j =  2                              :            45777
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908287
   j =  2                              :            45849
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 98                 :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.68
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.64
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.34
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.94
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.67
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.32
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.70
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.92
 p-value of test no 136                :  9.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.64
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.39
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.96
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.02
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.16
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.45
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.84
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.37
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.92
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.49
 p-value of test no 154                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.17
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.24
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.58
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.36
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.78
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.65
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.62
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.10
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.84
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.09
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.80
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.62
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.19
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.43
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.04
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.86
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.69
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.29
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.68
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.23
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.88
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.58
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.18
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.64
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.83
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.75
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.78
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.48
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.74
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.91
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.65
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.36
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.05
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.85
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.44
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.36
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000061966
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.80
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999924593
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:23.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187990035.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27205
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 7                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5570
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 19                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.29
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.64
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.84
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.73
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.61
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.00
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.75
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.81
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.86
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.20
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.27
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.14
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.05
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908054
   j =  2                              :            45970
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45272
 p-value of test no 71                 :    0.9977
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869272
   j =  1                              :        399909459
   j =  2                              :            45266
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
 p-value of test no 83                 :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-5
 p-value of test no 109                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.22
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.74
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.65
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.08
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.61
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.02
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.26
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.44
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.14
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.77
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17591.15
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.59
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.52
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.25
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.97
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.59
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.24
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.47
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.44
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.83
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.21
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.84
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.14
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.44
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.60
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.04
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.08
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.39
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.57
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.69
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.40
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.96
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.02
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.46
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.73
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.63
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.60
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.02
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 186                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 187                :  5.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.69
 p-value of test no 188                :  3.6e-3
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.52
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.58
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.73
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.58
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.39
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.78
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.42
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.95
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.90
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.99
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.24
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000021019
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.01
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999989123
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.97
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:16.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189038611.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27206
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 11                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.68
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    3.46
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     667
 p-value of test no 31                 :  3.8e-3
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.13
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.03
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.70
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.23
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.42
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.65
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.44
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7207.72
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.87
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.58
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.29
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.01
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.14
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46269
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870269
   j =  1                              :        399907467
   j =  2                              :            46259
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908464
   j =  2                              :            45762
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-3
 p-value of test no 103                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 105                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.96
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.01
 p-value of test no 120                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.80
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.57
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.29
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.13
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.21
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.86
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.68
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-4
 p-value of test no 138                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.84
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17635.03
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.43
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.73
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.79
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.92
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.19
 p-value of test no 154                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.68
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.40
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.15
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.21
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.42
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.12
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.82
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.37
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.34
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.70
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.35
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.56
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.31
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.42
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.57
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.95
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.38
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.90
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.65
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.75
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.07
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.80
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.09
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.76
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.26
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 208                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10318.15
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.56
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.00
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.58
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.72
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.35
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.82
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.32
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.12
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999960125
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.82
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000038200
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:50.77
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190021651.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27207
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 12                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    3.39
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.10
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.70
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.95
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.84
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.88
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.35
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.14
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.66
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.32
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.04
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.42
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.55
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.22
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.55
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.13
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908121
   j =  2                              :            45935
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45391
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869391
   j =  1                              :        399909221
   j =  2                              :            45385
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.61
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.91
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.27
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.84
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.64
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.09
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.17
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.74
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.84
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.05
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.49
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.64
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.46
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.09
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.45
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.83
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.64
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.61
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.39
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.61
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.07
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.90
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.50
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.24
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.59
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.38
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.52
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.23
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.75
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.29
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.03
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.88
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.46
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.46
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.06
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.53
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.74
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.65
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.89
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.05
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.70
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.25
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 180                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 181                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.60
 p-value of test no 182                :  1.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.14
 p-value of test no 183                :  8.4e-4    *****
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.33
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.97
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.99
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10221.40
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10234.91
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.11
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.86
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.86
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4324.24
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.79
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.82
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.94
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000023011
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.83
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000113722
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.18e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  82  LempelZiv, r = 0                8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190939155.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27208
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 6                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.87
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.96
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.97
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.82
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.94
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.92
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.76
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.42
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.47
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.62
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.10
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.43
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.81
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908052
   j =  2                              :            45968
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908076
   j =  2                              :            45956
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.21
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.13
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.58
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.83
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.45
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.79
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 131                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    5.10
 p-value of test no 132                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.15
 p-value of test no 133                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.01
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17294.27
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.84
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.50
 p-value of test no 147                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.71
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.59
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.66
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.90
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.45
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.16
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.96
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.09
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.77
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.98
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.57
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.29
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.78
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.74
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.96
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.84
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.33
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.65
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.49
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.36
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.69
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.12
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.73
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.06
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.66
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.35
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.02
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.26
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.15
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.64
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.88
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.97
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.61
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.17
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.69
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.45
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000048040
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.28
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000029899
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:52.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191889427.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27209
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.16
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.33
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.07
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.49
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.12
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.07
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.37
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.03
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.54
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.05
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.91
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.88
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.88
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.14
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.57
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45673
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908658
   j =  2                              :            45665
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907758
   j =  2                              :            46118
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.34
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.82
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.46
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.50
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.87
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.67
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.46
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.82
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.71
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.87
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.18
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.39
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.38
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.69
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.44
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.24
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.97
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.00
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.28
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.67
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.07
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.56
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.08
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.20
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.09
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.60
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.66
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.42
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.50
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.23
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.44
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.82
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.31
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.42
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.43
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.47
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.20
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.83
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.41
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.53
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.90
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 204                :  5.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 206                :  2.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.04
 p-value of test no 207                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.56
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
 p-value of test no 212                :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10332.75
 p-value of test no 215                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.27
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.10
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.35
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.58
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.17
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.62
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.52
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999941846
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.32
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000001738
 
 Normal statistic for number of bits   :   0.014
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:46.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192839699.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27210
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     249
 p-value of test no 37                 :    0.9986
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.58
 p-value of test no 40                 :  5.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.67
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.56
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.79
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.18
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.90
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.43
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.01
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.42
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.51
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.71
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.79
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.42
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.63
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908231
   j =  2                              :            45877
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 95                 :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9922
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.94
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.89
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.09
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.95
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.74
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.38
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.51
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.17
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.85
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.21
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.35
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.32
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.76
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.61
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.32
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.24
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.92
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.93
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.05
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.99
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.96
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.17
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.01
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.83
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.76
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.54
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.38
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.41
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.79
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.15
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.92
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.04
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.71
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.75
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.45
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.46
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.89
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.36
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.47
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.35
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.27
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.79
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.84
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.46
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.53
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.21
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.61
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.26
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.43
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.61
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.17
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.25
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999968165
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.83
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999945827
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:40.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193822739.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27211
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5559
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    3.74
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     249
 p-value of test no 37                 :    0.9986
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.42
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.78
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.17
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.33
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.74
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.76
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.30
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.94
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.98
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.60
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5214.86
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908208
   j =  2                              :            45887
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907778
   j =  2                              :            46108
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.72
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.17
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.97
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.47
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.33
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.50
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.33
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17592.62
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.58
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.88
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.77
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.49
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.20
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.02
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.10
 p-value of test no 155                :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.10
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.97
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.16
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.45
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.31
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.92
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.13
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.07
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.78
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.36
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.47
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.47
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.61
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.38
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.52
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.17
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.22
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.11
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.09
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.11
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.84
 p-value of test no 177                :    0.9978
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.50
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.90
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.59
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.94
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.05
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.08
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.24
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.10
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.72
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.80
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.52
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.23
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.53
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.70
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000109411
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.02
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999900830
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    2.23
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:54.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 C (L=50, r=25)      0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194936851.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27212
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 3                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.17
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.81
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.56
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.44
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.67
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.97
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.80
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.02
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.15
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.05
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 63                 :    0.9913
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.36
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.04
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.86
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4892.25
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908047
   j =  2                              :            45969
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9938
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.65
 p-value of test no 119                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.35
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.83
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.59
 p-value of test no 123                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.23
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.75
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.54
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.78
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.86
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 140                :    0.9989
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.65
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17326.27
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.79
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.07
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.80
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.89
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.99
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.36
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.19
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.37
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.90
 p-value of test no 156                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.34
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.30
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.77
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.35
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.36
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.31
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.82
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.05
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.94
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.25
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.50
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.31
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.10
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.85
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.14
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.89
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.08
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.40
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.29
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.33
 p-value of test no 198                :    0.9952
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.72
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.55
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.28
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.50
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 216                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.28
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.83
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.47
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.45
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.30
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.70
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.56
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999979136
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.34
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000047155
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:14.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195919891.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27213
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    3.18
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.79
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.43
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.48
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.21
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.55
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.78
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.81
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.19
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6934.28
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.79
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.48
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.08
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.04
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5153.71
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908482
   j =  2                              :            45750
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908005
   j =  2                              :            45993
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.91
 p-value of test no 115                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.98
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.37
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.90
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.24
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.49
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.27
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.34
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.04
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.94
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.45
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.29
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.94
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.26
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.59
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.47
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.73
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.87
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.84
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.14
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.97
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.77
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.96
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.16
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.08
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.31
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.06
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.09
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.91
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.32
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.16
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.69
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.48
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.45
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.69
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.17
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.16
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.08
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.14
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.67
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.32
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.13
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.05
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.91
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.90
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.43
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.83
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.39
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.88
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.12
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.73
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.87
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000115261
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.85
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000089722
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 248                :    0.9909
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:19.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196935699.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27214
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7114
 p-value of test no 18                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7557
 p-value of test no 19                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.90
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.63
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.00
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.10
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.94
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.96
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.56
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.01
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.55
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.39
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.62
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.87
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.39
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908624
   j =  2                              :            45682
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907893
   j =  2                              :            46052
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.66
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.64
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.21
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.85
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.88
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.31
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.59
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.62
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.94
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.20
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.46
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.80
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.17
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.49
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.47
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.01
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.78
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.64
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.98
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.98
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.72
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.30
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.76
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.45
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.07
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.18
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.21
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.53
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.66
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.28
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.35
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.40
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.78
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.71
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.86
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.57
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.24
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.16
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-4
 p-value of test no 185                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.52
 p-value of test no 196                :    0.9923
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.53
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.43
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.20
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.26
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.22
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.61
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.87
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.73
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.95
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.00
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.24
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999945731
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.01
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999947834
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.92e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:06.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197918739.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27215
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1214
 p-value of test no 11                 : 1 -  1.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334334
   j =  1                              :        599997572
   j =  2                              :             1214
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4497
 p-value of test no 16                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.27
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.87
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.82
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.96
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.74
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.64
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.15
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.86
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.07
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.10
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.94
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5249.02
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908113
   j =  2                              :            45939
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908188
   j =  2                              :            45903
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.77
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.00
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.14
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.68
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.49
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.67
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.30
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.54
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.73
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.05
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.28
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.79
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.35
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.15
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.71
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.31
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.13
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.25
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.64
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.91
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   98.33
 p-value of test no 159                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.07
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.79
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.43
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.32
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.67
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.17
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.52
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.39
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.53
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.73
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.31
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.44
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.89
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.84
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.97
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.20
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.19
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.75
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.57
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.16
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10229.40
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.57
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.61
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.19
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.08
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.48
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.57
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.68
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000068674
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.82
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999962531
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 245                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    4.82
 p-value of test no 247                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.94
 p-value of test no 248                :    0.9984
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:36.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  1.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198901779.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27216
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 4                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 14                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7058
 p-value of test no 19                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.9910
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.30
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.63
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.50
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.14
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.13
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.70
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.53
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.49
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.97
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.62
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.30
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.64
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.19
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.91
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908627
   j =  2                              :            45685
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908438
   j =  2                              :            45778
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.67
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.10
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.92
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 127                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 128                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   68.48
 p-value of test no 129                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.50
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.81
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17165.64
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.19
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.20
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.43
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.02
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.59
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.10
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.55
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.95
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.56
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.96
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.79
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.80
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.87
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.36
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.12
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.01
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.17
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.23
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.24
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.11
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.48
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.71
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.28
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.07
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.14
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.82
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.64
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.31
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.58
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.11
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.56
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.30
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.99
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.88
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.44
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.14
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.52
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.04
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.02
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.23
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.71
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000052369
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.90
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999829883
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-4
 p-value of test no 240                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:32.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199884819.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27217
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 4                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9928
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.11
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.16
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.23
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.26
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.07
 p-value of test no 52                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.80
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.92
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.37
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.35
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.35
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.62
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.60
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.46
 p-value of test no 66                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.08
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.57
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907925
   j =  2                              :            46030
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908665
   j =  2                              :            45657
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.41
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.11
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.95
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.67
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.54
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.21
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.93
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.71
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.95
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.29
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.14
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.23
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.85
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.53
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.47
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.49
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.15
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.07
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.90
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.80
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.81
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.30
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.95
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.53
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.62
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.66
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.18
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.67
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.75
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.89
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.29
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.91
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.61
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.36
 p-value of test no 171                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.86
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.18
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.97
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.94
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.57
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.77
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.85
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.40
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.54
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.89
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.12
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 225                :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.71
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.87
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.70
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.12
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11573.49
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.52
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000108136
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.93
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000032887
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:07.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201031699.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27218
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7087
 p-value of test no 21                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.04
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.34
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.82
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.68
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.34
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.94
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.44
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1543.45
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.08
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.78
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.59
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.72
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.32
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907526
   j =  2                              :            46228
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908098
   j =  2                              :            45948
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.12
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.22
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.01
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.23
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.20
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.95
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.53
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.62
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.34
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.86
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.16
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.00
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.87
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.78
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.37
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.27
 p-value of test no 150                :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.11
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.64
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.87
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.64
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.01
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.61
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.33
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.90
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.97
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.57
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.11
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.63
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.29
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.54
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.86
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.30
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.31
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.96
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.23
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.95
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.09
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.48
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.39
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.65
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.88
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.24
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 206                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  146.09
 p-value of test no 207                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.83
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.04
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.04
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.19
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.96
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.86
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.83
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.10
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.10
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000045037
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.53
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999929792
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:22.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202113043.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27219
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.54
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.10
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.77
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.03
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.72
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.94
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.21
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.01
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7230.71
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.48
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.96
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.47
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.35
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.93
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46357
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870357
   j =  1                              :        399907287
   j =  2                              :            46355
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46237
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870237
   j =  1                              :        399907528
   j =  2                              :            46233
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.61
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.72
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.70
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.74
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.40
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.84
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.25
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.83
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
 p-value of test no 138                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.96
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.16
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.63
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.84
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.40
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.69
 p-value of test no 149                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.83
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.42
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.52
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.70
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.62
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.06
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.82
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.08
 p-value of test no 159                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.70
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.86
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.42
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.48
 p-value of test no 163                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.84
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.14
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.15
 p-value of test no 166                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.55
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.29
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.97
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.07
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.26
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.13
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.80
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.42
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.99
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.89
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.95
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.52
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.11
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.47
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.78
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.84
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.44
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.24
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.03
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.38
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.15
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999903467
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.74
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000111982
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:56:59.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203194387.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27220
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.05
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.08
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.43
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.74
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.61
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.70
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.09
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.72
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.97
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.74
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.85
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.22
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908404
   j =  2                              :            45792
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908189
   j =  2                              :            45898
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  8.9e-3
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.87
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.07
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.16
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.69
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.89
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.85
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.51
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.23
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17672.64
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.98
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.86
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.97
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.14
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.17
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.84
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.65
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.75
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.59
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.42
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.92
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.68
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.14
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.68
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.36
 p-value of test no 161                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.58
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.32
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.12
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.87
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.30
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.94
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.69
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.17
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.07
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.97
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.71
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.52
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.23
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.93
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.48
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.06
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.22
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.34
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.75
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.30
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4712.25
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.02
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.98
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.37
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.82
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.12
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.04
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000025012
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000031879
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:15:25.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183631892.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27221
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 11                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.34
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    2.97
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.21
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.77
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.05
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.65
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :  101.56
 p-value of test no 52                 :  9.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.24
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.16
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.70
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1312.31
 p-value of test no 56                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.89
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.23
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.16
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.68
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5174.16
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908463
   j =  2                              :            45761
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46178
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870178
   j =  1                              :        399907645
   j =  2                              :            46176
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.11
 p-value of test no 115                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.65
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.58
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.90
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.60
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.16
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.47
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.12
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.47
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17546.36
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.58
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.63
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.35
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.17
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.45
 p-value of test no 151                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.22
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.96
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.63
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.55
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.42
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.61
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.37
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.42
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.34
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.59
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.79
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.23
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.05
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.73
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4750.81
 p-value of test no 168                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.96
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.98
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.66
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.20
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.53
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.69
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.67
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.95
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.22
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.21
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.33
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.99
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5100.84
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.82
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.22
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.22
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.31
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.19
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.22
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000033190
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.53
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999911642
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:57.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         9.7e-5
  55  SampleCorr, k = 1               0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184778772.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27222
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 11                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.28
 p-value of test no 22                 :  7.5e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.42
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.06
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.16
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.96
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.22
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.06
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.12
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.67
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-4
 p-value of test no 62                 :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 64                 :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  106.62
 p-value of test no 65                 :  2.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.32
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5192.42
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908592
   j =  2                              :            45692
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907917
   j =  2                              :            46040
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.61
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.14
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.42
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.44
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.20
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.36
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.13
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.08
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.59
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.74
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.97
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.66
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.92
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.21
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.28
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.55
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.97
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.23
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.54
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.07
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.82
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.62
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.47
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.88
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.90
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.11
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.38
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.53
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.77
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.50
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.32
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.40
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.97
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.41
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.47
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.36
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.62
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.71
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.63
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.80
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.48
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.02
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.23
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.26
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.95
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.10
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.75
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.86
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
 p-value of test no 220                :    0.9972
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4612.04
 p-value of test no 222                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5090.86
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.47
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3963.60
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.37
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.31
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.83
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000165007
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.50
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000138508
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 251                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:39.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            7.5e-4
  39  Run, r = 15                     2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185597972.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
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                     Run no 27223
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 9                  :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.25
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.32
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.61
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.64
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.21
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.59
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.84
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.09
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.30
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.25
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.57
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5204.03
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908233
   j =  2                              :            45876
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45278
 p-value of test no 71                 :    0.9975
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869278
   j =  1                              :        399909446
   j =  2                              :            45274
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.73
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.05
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.21
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.96
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.77
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.44
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.80
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.11
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.77
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.53
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.03
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.10
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.88
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.13
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.51
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.67
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.82
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.31
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.95
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.48
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.23
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.91
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.78
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.13
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.71
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.61
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.14
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.49
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.59
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.48
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.49
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.83
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.01
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.75
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.05
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.16
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.23
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.72
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.41
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.91
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.62
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.43
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.88
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.55
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.93
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.12
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9781.44
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.51
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4673.80
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.29
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.45
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3868.71
 p-value of test no 228                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.62
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12129.04
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.01
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000091495
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.15
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999814514
 
 Normal statistic for number of bits   :   -1.47
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    2.56
 p-value of test no 239                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:14.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186482708.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27224
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.79
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.26
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.42
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.83
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.12
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.47
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.14
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.80
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.88
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.30
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6888.34
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.23
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.94
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.93
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.56
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908501
   j =  2                              :            45748
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908636
   j =  2                              :            45679
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-5
 p-value of test no 109                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.97
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  107.47
 p-value of test no 120                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.32
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.22
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.13
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.15
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.36
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.78
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.80
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.79
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.47
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.76
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.87
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.48
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.98
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.67
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.27
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.72
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.79
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.38
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.97
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.56
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.31
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.51
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.07
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.69
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.18
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.73
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.19
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.83
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.27
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.37
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.46
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.86
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.10
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.75
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.45
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.74
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.98
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.79
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.17
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.81
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.81
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.08
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.91
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5053.46
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.16
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4365.55
 p-value of test no 227                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.04
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.08
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.00
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.86
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999956021
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.24
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000082915
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-4
 p-value of test no 241                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.43
 p-value of test no 243                :    0.9924
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:21.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187727892.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27225
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 3                  :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     977
 p-value of test no 25                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.12
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.65
 p-value of test no 48                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.16
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.58
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.90
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.87
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.17
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.29
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.32
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-3
 p-value of test no 58                 :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.60
 p-value of test no 61                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.86
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.61
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5254.31
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907724
   j =  2                              :            46138
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908226
   j =  2                              :            45881
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 73                 :    0.9909
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.86
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.96
 p-value of test no 120                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.62
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.53
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.38
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.48
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.96
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.56
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.33
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.79
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.94
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.83
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.48
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.49
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.99
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.72
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.58
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.39
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.44
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.38
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.77
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.70
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.35
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.85
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.14
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.78
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.58
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.07
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.97
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.67
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.48
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.16
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.62
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.33
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.84
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.66
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 186                :    0.9975
 
 Anderson-Darling statistic = A2       :    5.54
 p-value of test no 187                :  1.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.29
 p-value of test no 188                :    0.9995    *****
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.24
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.90
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.47
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.51
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.39
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.20
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.73
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.30
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.76
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.67
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.74
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000056401
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.54
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000142954
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9935
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:42.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            0.9992 
  83  LempelZiv, r = 15               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188907540.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27226
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 6                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.41
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.94
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.73
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.10
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.11
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.48
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.94
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.55
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.65
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.31
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.50
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.39
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.22
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908074
   j =  2                              :            45963
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46311
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870311
   j =  1                              :        399907380
   j =  2                              :            46307
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.69
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.94
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.14
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.35
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.29
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.44
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.66
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.70
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.01
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.31
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.72
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.18
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.21
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.12
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.57
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.87
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.70
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.97
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.55
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.75
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  611.34
 p-value of test no 158                :  4.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.41
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.33
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.82
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.71
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.16
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.29
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.18
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.87
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.15
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.59
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.82
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.28
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.95
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.70
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.93
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.19
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.23
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.71
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.65
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.94
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.05
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.99
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.50
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.76
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.97
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 224                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.52
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.87
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.87
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12014.36
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.98
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.68
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999971609
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.31
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999964571
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.18
 p-value of test no 254                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:03.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 J (L=1000, r=0)     4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189825044.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27227
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 6                  :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4136
 p-value of test no 16                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.12
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.66
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.52
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.68
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.52
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.34
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.72
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.77
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.23
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.62
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.42
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.90
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.80
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46148
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870148
   j =  1                              :        399907710
   j =  2                              :            46136
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908742
   j =  2                              :            45626
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.08
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.38
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.06
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.84
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.14
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.42
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.03
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.12
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.43
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.05
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.07
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.96
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.49
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.89
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.24
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.27
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.77
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.86
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.74
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.18
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.77
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.41
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.32
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.30
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.18
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.64
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.37
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.63
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.27
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.05
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.64
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.43
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.29
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.01
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.51
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.27
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.49
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.70
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.40
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 208                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10225.14
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.78
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 216                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4671.97
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.09
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.90
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.78
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12115.91
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.04
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.74
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000004453
 
 Normal statistic for number of bits   :   0.035
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.07
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000058252
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:42.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190709780.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27228
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.75
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.95
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.48
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.91
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.10
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.98
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.64
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.65
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.88
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.43
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.62
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.45
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.70
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.83
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.20
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.48
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908332
   j =  2                              :            45825
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907838
   j =  2                              :            46075
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-4
 p-value of test no 109                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.90
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.16
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.25
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.80
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.75
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.93
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.32
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.51
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17739.34
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.49
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.47
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.77
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.56
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.47
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.75
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.27
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.20
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.76
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.53
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.92
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.08
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.71
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.50
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.67
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.53
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.99
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.49
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.04
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.78
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5184.04
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.92
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.07
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.09
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.78
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.73
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.29
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.62
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.16
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.26
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.18
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.77
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.08
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.93
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.77
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.01
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.49
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.94
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.21
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.09
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11544.26
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.83
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999996830
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.72
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999938978
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.14
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:16.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191660052.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27229
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9970
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.58
 p-value of test no 49                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.94
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.22
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.94
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.36
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6954.66
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.83
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.93
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.42
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.67
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908649
   j =  2                              :            45674
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907966
   j =  2                              :            46011
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.40
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.23
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.54
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.23
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.17
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.97
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.23
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.56
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.76
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17177.51
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.11
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.76
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.99
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.17
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.80
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.88
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.12
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.58
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.38
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.38
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.18
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.96
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.92
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.20
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.33
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.26
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.90
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.63
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.59
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.42
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.92
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.49
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.28
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.70
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.13
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.23
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.36
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.70
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.59
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.40
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.44
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.92
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.71
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.18
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.66
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.87
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.72
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.63
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12176.82
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.98
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.62
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000029815
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.37
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999939281
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    2.08
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:34.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192610324.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27230
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.55
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.73
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.57
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.32
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.90
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.94
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.35
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.93
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.80
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.62
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.16
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.74
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.65
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.67
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908085
   j =  2                              :            45953
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45432
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869432
   j =  1                              :        399909141
   j =  2                              :            45422
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.86
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.10
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.51
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.62
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.23
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.04
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.81
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.95
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   15.89
 p-value of test no 136                :  3.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.09
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17236.69
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.40
 p-value of test no 146                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.05
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.69
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.62
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.49
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.18
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.66
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.07
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   92.92
 p-value of test no 159                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.34
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.84
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.59
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.65
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.82
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.70
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.06
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.19
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.08
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.12
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.60
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.90
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.01
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.29
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.93
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.07
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.80
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.25
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.33
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.91
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.21
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.53
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.25
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.49
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.50
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5127.22
 p-value of test no 226                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.00
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4321.60
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12065.27
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.44
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.44
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000291148
 
 Normal statistic for number of bits   :    2.30
 p-value of test no 232                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.89
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000095512
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 238                :    0.9900
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:46.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193593364.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27231
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.01
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.32
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.93
 p-value of test no 49                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.56
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.18
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.04
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.99
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.20
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.47
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.84
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.71
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.19
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.68
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.88
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.47
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907980
   j =  2                              :            46004
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908411
   j =  2                              :            45793
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.91
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.31
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.46
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.00
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.56
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.68
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.06
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.82
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.45
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17374.66
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.52
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.52
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.12
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.55
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.92
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.35
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.66
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.19
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.66
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.82
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.00
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.68
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.43
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.29
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.67
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.52
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.25
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.33
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.85
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.07
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.95
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  495.66
 p-value of test no 172                :  1.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.17
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.06
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.25
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.38
 p-value of test no 176                :    0.9922
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.63
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.78
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.72e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.16
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.74
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.90
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.92
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.67
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5073.68
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.42
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.05
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.82
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.03
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.87
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999929099
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.00
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999926447
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:34.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194576404.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27232
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5241
 p-value of test no 13                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7072
 p-value of test no 21                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9908
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.73
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   44.25
 p-value of test no 48                 :  5.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.24
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.30
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.15
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.99
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.51
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.70
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.17
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.33
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.31
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.75
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.94
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.60
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.72
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4917.53
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45480
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909042
   j =  2                              :            45476
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907839
   j =  2                              :            46073
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 90                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
 p-value of test no 104                :    0.9975
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.60
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.02
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.53
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.59
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.03
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.75
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.23
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.18
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.29
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.49
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.35
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.44
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.13
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.28
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.64
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.98
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.36
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.45
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.56
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.98
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.50
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.70
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.53
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.27
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.57
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.36
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.19
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.00
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.17
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.75
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.78
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.73
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.97
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.21
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.99
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.75
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.25
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.52
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.89
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.09
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.64
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.54
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.05
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.13
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.35
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.69
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.65
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.47
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.94
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.31
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.53
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000016192
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.91
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999840677
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 250                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 253                :  4.7e-3
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:56.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195526676.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27233
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1494
 p-value of test no 12                 :  2.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334614
   j =  1                              :        599997012
   j =  2                              :             1494
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.67
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.35
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.42
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.92
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.41
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.69
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.06
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.53
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.71
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.85
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.37
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.70
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.26
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908831
   j =  2                              :            45583
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908145
   j =  2                              :            45926
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 97                 :  5.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    7.09
 p-value of test no 99                 :  3.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-4
 p-value of test no 113                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.46
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.71
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.73
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.85
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.21
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.81
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.18
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.56
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17461.39
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.67
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.52
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.37
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.50
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.05
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.52
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.94
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.11
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.98
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.07
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.61
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.79
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.80
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.04
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.20
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.75
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.97
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.01
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.96
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.04
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.87
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.87
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.79
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.40
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.71
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.07
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.43
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.27
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.18
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.52
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.84
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.40
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.40
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.81
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.03
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.34
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.40
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.44
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12338.47
 p-value of test no 230                :  4.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000085516
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.41
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999853046
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:52.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.8e-4
  49  MaxOft AD, t = 32               3.2e-4
  100  HammingIndep, L=1200, r=25      4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196509716.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27234
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 8                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.56
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.25
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.60
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.54
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.47
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.04
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.16
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.72
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.33
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.10
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.66
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.52
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.29
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.88
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.11
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908113
   j =  2                              :            45942
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908241
   j =  2                              :            45875
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.69
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.90
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.34
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.07
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.70
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.62
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.18
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.14
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.79
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.71
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.17
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.42
 p-value of test no 137                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.09
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 142                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16967.63
 p-value of test no 145                :    0.9937
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.25
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.40
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.14
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.79
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.39
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.27
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.56
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.31
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.17
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.78
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.79
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.31
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.52
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.17
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.81
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.63
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.00
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.17
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.70
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.64
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.67
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.62
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.21
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.22
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.17
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.36
 p-value of test no 176                :    0.9924
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.04
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.22
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.64
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.00
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.66
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.80
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 212                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 214                :  3.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9622.33
 p-value of test no 215                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.15
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.85
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4352.69
 p-value of test no 227                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.81
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.76
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.78
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.27
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000066295
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.88
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000050881
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:42.34
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197459988.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27235
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 9                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    3.72
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.71
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.20
 p-value of test no 51                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.19
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.63
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.08
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1333.56
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.84
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.15
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.31
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.92
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.54
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.34
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908070
   j =  2                              :            45962
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.09
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.92
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.44
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.39
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   58.65
 p-value of test no 125                :  9.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.85
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
 p-value of test no 131                :    0.9932
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.30
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.93
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.02
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17345.71
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.19
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.05
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.39
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.75
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.87
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.99
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.20
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.37
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.71
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.97
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.98
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.16
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.67
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.18
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.98
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.54
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.49
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.19
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.82
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.32
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.53
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.21
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.09
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5270.44
 p-value of test no 173                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.28
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.62
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.04
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.76
 p-value of test no 177                :    0.9971
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.02
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.84
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.66
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.77
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.92
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.41
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.86
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.21
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.25
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.23
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.89
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.45
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.29
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999808583
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.63
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000029611
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 235                :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.20
 p-value of test no 249                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:00.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198410256.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27236
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5302
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    3.34
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    5.14
 p-value of test no 27                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.89
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.21
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.68
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.41
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.03
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.11
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.84
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.64
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.15
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.99
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.24
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4834.08
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907903
   j =  2                              :            46041
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907964
   j =  2                              :            46015
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.86
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.67
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.53
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.05
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.75
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.69
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.58
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.64
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.33
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.66
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.58
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
 p-value of test no 142                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17855.74
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.29
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.97
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.61
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.42
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.55
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.81
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.93
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.30
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.18
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.43
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.42
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.57
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.80
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.79
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.20
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.87
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.29
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.91
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.90
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.65
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.22
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.96
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.73
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.63
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.62
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.94
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.32
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.40
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.72
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.17
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.64
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.06
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.76
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.99
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.61
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.80
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9777.82
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.06
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.25
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.25
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.07
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.10
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.39
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.18
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000004522
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.85
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000076216
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:03.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199393296.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27237
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.08
 p-value of test no 22                 :  2.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.07
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.75
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.18
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.04
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.69
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.63
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  520.60
 p-value of test no 55                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.36
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.14
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.30
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.66
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.57
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.34
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.43
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908409
   j =  2                              :            45794
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908777
   j =  2                              :            45607
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.28
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.28
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.42
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.94
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.63
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.52
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.62
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.68
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.75
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.68
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.74
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.90
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.25
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.62
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.13
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.56
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.97
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.68
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.23
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.97
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.42
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.55
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.16
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.77
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.88
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.73
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.48
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.05
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.98
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.41
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.06
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.69
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.50
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.60
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.32
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.47
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.77
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.41
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.75
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 206                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.29
 p-value of test no 207                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.62
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10260.05
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.44
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.34
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.59
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.08
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.22
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.40
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.31
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000056341
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.78
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000019333
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:47.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200409104.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27238
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 33                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.96
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.66
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.73
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.04
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.42
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.19
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.19
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6840.88
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.57
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.73
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.46
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.00
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45531
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869531
   j =  1                              :        399908941
   j =  2                              :            45525
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908023
   j =  2                              :            45987
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.06
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.50
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.88
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.98
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.04
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.64
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.67
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.62
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.59
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.88
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.88
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.41
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.17
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.99
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.45
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.12
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.73
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.71
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.59
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.35
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.95
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.73
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.45
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.03
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.39
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.49
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.95
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.53
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.26
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.63
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.58
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.42
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.31
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.95
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.98
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.67
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.54
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.39
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.79
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.50
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.36
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9786.21
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.31
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.15
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.60
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.55
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.48
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.56
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.28
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.82
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000001855
 
 Normal statistic for number of bits   :   0.015
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.38
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999961421
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 235                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:13.85
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201424912.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27239
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.46
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.49
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.31
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.79
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.11
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.07
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.91
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.64
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.76
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.44
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.35
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.84
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.80
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.28
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.37
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46132
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907738
   j =  2                              :            46128
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.49
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.54
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.33
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.07
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.99
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.94
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.62
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.10
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.43
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17622.70
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.68
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.97
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.91
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.21
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.94
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.75
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.75
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.58
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.82
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.70
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.65
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.04
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.80
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.83
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.57
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.86
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.82
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.65
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.16
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.16
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.12
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.14
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.06
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.78
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.86
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.28
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.55
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.77
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.37
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.57
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.34
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.14
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.77
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.23
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.80
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.02
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.73
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.03
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.34
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.54
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.23
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.26
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000155077
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.53
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999912143
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:01.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202407952.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27240
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4124
 p-value of test no 14                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7525
 p-value of test no 20                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.04
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.57
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.15
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.82
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.27
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.63
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.96
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 60                 :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.21
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.53
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.00
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.69
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.56
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908004
   j =  2                              :            45992
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908419
   j =  2                              :            45777
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.72
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.82
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.61
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.08
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.05
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.04
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.89
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.72
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.84
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.19
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.70
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.41
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.33
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.45
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.03
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.54
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.68
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.47
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.23
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.96
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.51
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.03
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.31
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.65
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.21
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.45
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.28
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.45
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.96
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.53
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.54
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.51
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.31
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.35
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.22
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.11
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.74
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.11
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.81
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.91
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 186                :    0.9933
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.83
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.90
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.23
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.56
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.71
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.12
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4307.98
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.09
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.50
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.02
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.22
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000121390
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.69
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000058252
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:26.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183664661.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27241
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 10                 :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.11
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.36
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.97
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.26
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.74
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.72
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.73
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.87
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.66
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.21
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.76
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.98
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.33
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908074
   j =  2                              :            45957
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908531
   j =  2                              :            45733
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.07
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.50
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.39
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.75
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.19
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.85
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.65
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.43
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.11
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.41
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.34
 p-value of test no 137                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.83
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.16
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.77
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.12
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.69
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.61
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.86
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.44
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.58
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.06
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.83
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.72
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.30
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.36
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.58
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.62
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.43
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.92
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  579.10
 p-value of test no 163                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.46
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.78
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.94
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.38
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.48
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.90
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.89
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.80
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.85
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.90
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.18
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.97
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.49
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.18
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.78
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.68
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.39
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.69
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.61
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.32
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.06
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.49
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.64
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.41
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.33
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.25
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.53
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999920603
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.48
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000046060
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:59.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184188949.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27242
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.30
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.33
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.56
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.69
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.96
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.18
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.42
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.44
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.48
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.86
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.24
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.04
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.96
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5264.63
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908172
   j =  2                              :            45908
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908199
   j =  2                              :            45893
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-4
 p-value of test no 72                 :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9901
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.46
 p-value of test no 115                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.73
 p-value of test no 116                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.04e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.66
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.53
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.85
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.52
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.71
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.88
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.57
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.24
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.67
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.92
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.31
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.28
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.70
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.47
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.51
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.43
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.27
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.21
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.78
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.32
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.74
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.81
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.23
 p-value of test no 160                :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.02
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.42
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.28
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.20
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.71
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.72
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.51
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.45
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.19
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.93
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.96
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.06
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.12
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.96
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.91
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.71
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.53
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9738.07
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.56
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.36
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.49
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.90
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.16
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.52
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.59
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.39
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999991016
 
 Normal statistic for number of bits   :  -0.071
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.78
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999984809
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:15:35.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185237525.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27243
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.24
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.82
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.88
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.92
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.66
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.92
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.76
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.08
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.02
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.24
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.29
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908440
   j =  2                              :            45777
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45635
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869635
   j =  1                              :        399908735
   j =  2                              :            45625
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.46
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.45
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.83
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.10
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.55
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.50
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.02
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.52
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.68
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.69
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.90
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.79
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.74
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.45
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.31
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.59
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.31
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.92
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.68
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.32
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.16
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.78
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.21
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.91
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.37
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.22
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.26
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.63
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.82
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.57
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.33
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.70
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.59
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.16
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.21
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.30
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.65
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.70
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.01
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.37
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.30
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.10
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.90
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.28
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.55
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.12
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.68
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.16
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.73
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.55
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000062281
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.12
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000111655
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:44.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187006997.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27244
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 42                 :    0.9982
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.14
 p-value of test no 47                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.74
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.39
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.96
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.27
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.50
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.49
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.96
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.98
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.78
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.96
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.07
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.27
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.65
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907995
   j =  2                              :            45995
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908075
   j =  2                              :            45952
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
 p-value of test no 110                :  7.0e-3
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 111                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.43
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.26
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.74
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.44
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.20
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.12
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.72
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.94
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.95
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17564.11
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.40
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.74
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.04
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.00
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.40
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.15
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.01
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.48
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.31
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.69
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.77
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.25
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.49
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.54
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.16
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.99
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.67
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.22
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.26
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.03
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.85
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.48
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.69
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.31
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.78
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.67
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.55
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.31
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.08
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.23
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.96
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.32
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.78
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.26
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.43
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.68
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.31
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.13
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.63
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000060460
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.08
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000230626
 
 Normal statistic for number of bits   :    1.82
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.072
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:30.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188022805.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27245
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 3                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 10                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9939
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.60
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.20
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.31
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.13
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.93
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.63
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.91
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.46
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.69
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.66
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.71
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.99
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.15
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.24
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908631
   j =  2                              :            45680
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.21
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.23
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.62
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.87
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.75
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.41
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.19
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.13
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.95
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.64
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.33
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.50
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.83
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.72
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.56
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.58
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.18
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   95.89
 p-value of test no 157                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.54
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.89
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.47
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.72
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.46
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.52
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.73
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.67
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.81
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.66
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.20
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.32
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.21
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.74
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.29
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.46
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.28
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.35
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.60
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.76
 p-value of test no 198                :  5.4e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.42
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.61
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.65
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.10
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.65
 p-value of test no 217                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 218                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.05
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.06
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.38
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.86
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.21
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.43
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.80
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000019306
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.72
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999921203
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    2.62
 p-value of test no 244                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    2.40
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:43.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 M (L=1000, r=0)     0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189005845.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27246
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.77
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.53
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.60
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.82
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.27
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.73
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.32
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.56
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.63
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.12
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.77
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.28
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.59
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.11
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.84
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.55
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907940
   j =  2                              :            46030
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908147
   j =  2                              :            45925
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.84
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   36.94
 p-value of test no 120                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.83
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.70
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.62
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.71
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.85
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.79
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 130                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.09
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.26
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.22
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.31
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.95
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.31
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.77
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.44
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.85
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.06
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.88
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.13
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.36
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.23
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.12
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.99
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.42
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.61
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.71
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.08
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.75
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.78
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.35
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.17
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.89
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.12
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.96
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.45
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.39
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.43
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.45
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.88
 p-value of test no 178                :  2.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.81
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.05
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.00
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.35
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.75
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.12
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.93
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.17
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.40
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.52
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.68
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999975107
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.92
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000059800
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:47.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189988885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27247
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1491
 p-value of test no 4                  :  3.7e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334611
   j =  1                              :        599997018
   j =  2                              :             1491
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.15
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.39
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.06
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.05
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.23
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.67
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1532.87
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.94
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.74
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.70
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.32
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.33
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46304
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870304
   j =  1                              :        399907403
   j =  2                              :            46282
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908284
   j =  2                              :            45855
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.96
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.91
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.79
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.79
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.58
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.28
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.75
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.15
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.07
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.97
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.57
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.04
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.05
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.79
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.32
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.74
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.56
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.73
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.94
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.92
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.25
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.31
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.52
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.71
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.08
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.23
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.70
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.45
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.66
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.49
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.01
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.02
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.31
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.75
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.46
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.59
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.56
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.70
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.92
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.11
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.15
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.75
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.97
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.47
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.10
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.47
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.40
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.59
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.74
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.78
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.01
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.23
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.47
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.30
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000001885
 
 Normal statistic for number of bits   :   0.015
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.04
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999925085
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:06.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            3.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190971925.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27248
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.20
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.87
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     346
 p-value of test no 37                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.28
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.38
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.72
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.38
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.69
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.68
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.44
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.63
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.85
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.49
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.31
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.62
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.36
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.68
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.42
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908563
   j =  2                              :            45711
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908324
   j =  2                              :            45835
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-4
 p-value of test no 103                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  3.7e-3
 
 Anderson-Darling statistic = A2       :    5.08
 p-value of test no 105                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.95
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.63
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.62
 p-value of test no 122                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.97
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.86
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.71
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.05
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.11
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.89
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 139                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 140                :  6.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   92.86
 p-value of test no 141                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17514.38
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.92
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.92
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.43
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.28
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.96
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.61
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.44
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.04
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.81
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.65
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.59
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.56
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.03
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.27
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.73
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.77
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.62
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.35
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.33
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.63
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.34
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.66
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.94
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.84
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.93
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.20
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.43
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.60
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.48
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.33
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.78
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.97
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.88
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.96
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.28
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.69
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.59
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.54
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.98
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.08
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.77
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999881801
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.04
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000117025
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.16
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.100
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191954965.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27249
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   22.22
 p-value of test no 47                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.72
 p-value of test no 48                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.15
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.25
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.32
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.45
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.08
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.10
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.07
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.87
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.74
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.79
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.36
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5228.47
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907776
   j =  2                              :            46100
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908060
   j =  2                              :            45964
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.52
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.45
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.91
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.72
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.62
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.20
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.64
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.54
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.43
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.65
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17165.72
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.74
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.52
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.48
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.56
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.34
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.40
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.11
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.53
 p-value of test no 156                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.68
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.40
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.45
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.29
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.33
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.90
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.65
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.47
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.43
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.12
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.02
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.57
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.10
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.27
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.59
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.79
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.67
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.70
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.12
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.37
 p-value of test no 176                :  4.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.94
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 201                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 202                :  5.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.42
 p-value of test no 203                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.32
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.17
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.74
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 217                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.33
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.93
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.97
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.34
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.16
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.41
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.26
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000069322
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.05
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000117730
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:31.72
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192905237.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27250
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.94
 p-value of test no 46                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.36
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.88
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.55
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.66
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.40
 p-value of test no 53                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.77
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.19
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1532.53
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6855.32
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.63
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.91
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.61
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.85
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.79
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908366
   j =  2                              :            45814
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908195
   j =  2                              :            45898
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  7.7e-3
 
 Anderson-Darling statistic = A2       :    3.89
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.10
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.89
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.82
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.37
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.30
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.45
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.70
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.52
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.44
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.70
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.48
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.54
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.35
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.19
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.96
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.92
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.92
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.06
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.63
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.90
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.64
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.50
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.78
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.44
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.86
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.71
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.56
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.09
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.46
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.84
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.65
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.94
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.76
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.42
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.17
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.39
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.16
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.78
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.60
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.75
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.55
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 205                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.11
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.76
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.75
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.51
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.45
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.07
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.44
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.28
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11535.37
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.88
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999980222
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.44
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999918140
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.56
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193855509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27251
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.92
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.67
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.84
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.34
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.52
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.50
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.94
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.73
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.79
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7189.79
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.54
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.22
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.84
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.86
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908212
   j =  2                              :            45888
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907970
   j =  2                              :            46012
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 115                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.48
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.98
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.26
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.13
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.57
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.19
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.45
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.73
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.28
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.60
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.56
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.12
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.26
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.43
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.29
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.17
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.43
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.68
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.29
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.41
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.51
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.50
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.02
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.62
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.77
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  201.84
 p-value of test no 162                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.77
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.08
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.57
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.62
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.62
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.21
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.49
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.39
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.40
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.43
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.96
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.70
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.78
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.60
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-4
 p-value of test no 185                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.80
 p-value of test no 188                :  2.5e-3
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.85
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.78
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.96
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.01
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.84
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.74
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.73
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.98
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.34
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.34
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.33
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999849821
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.27
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000104095
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:49.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194805781.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27252
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.66
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.10
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.27
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.39
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.39
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.03
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.09
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.11
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.59
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.30
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.50
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.49
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.14
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45552
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908899
   j =  2                              :            45546
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46197
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907613
   j =  2                              :            46183
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.59
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.47
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.48
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.21
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.08
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.17
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.50
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.19
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.40
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.37
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.28
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.91
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.65
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.12
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.63
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.08
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.45
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.10
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.44
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.99
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.80
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.08
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.22
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.08
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.05
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.84
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.99
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.58
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.75
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.52
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.48
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.64
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.18
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.00
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.25
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.94
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.74
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.66
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.23
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.61
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.31
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.23
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.69
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.09
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.49
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.85
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.28
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.30
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.18
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.62
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.27
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.47
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11570.33
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.35
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.23
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999942584
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999981500
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.22
 p-value of test no 244                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:06.73
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195952661.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27253
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.06
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.12
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.79
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.91
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.76
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.00
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.11
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6800.45
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.66
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.67
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.43
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.48
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45584
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908833
   j =  2                              :            45582
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908244
   j =  2                              :            45872
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.71
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.81
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.88
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.12
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.72
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.77
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.10
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.07
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.70
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.38
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.81
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.02
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.43
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.00
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.63
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.69
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.65
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.62
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.88
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.78
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.43
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.12
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.98
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.62
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.01
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.06
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.77
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.00
 p-value of test no 170                :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.30
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.00
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.27
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.15
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.14
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.99
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.27
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.76
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.16
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.48
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 212                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 213                :    0.9932
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 214                :  7.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9614.11
 p-value of test no 215                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.60
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.29
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.01
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.85
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.68
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12139.03
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.53
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000204163
 
 Normal statistic for number of bits   :    1.61
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.98
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999840542
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.40
 p-value of test no 253                :    0.9917
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:03.43
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196870165.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27254
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.12
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.63
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.29
 p-value of test no 52                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.25
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.16
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.58
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1519.86
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.32
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.63
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.13
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.07
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.75
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.87
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908607
   j =  2                              :            45695
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46379
 p-value of test no 71                 :  1.0e-2
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870379
   j =  1                              :        399907250
   j =  2                              :            46363
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.97
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.48
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.69
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.58
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.63
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.68
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.53
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.18
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.51
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.68
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.67
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.24
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.39
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.87
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.46
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.80
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.68
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.67
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.12
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.85
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.08
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.63
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.24
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.40
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.15
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.34
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.70
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.29
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.04
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.63
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.65
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.85
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.76
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.82
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.74
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.21
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.25
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.17
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    2.14
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.23
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-4
 p-value of test no 200                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.25
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 205                :    0.9902
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.82
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.72
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.65
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.48e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.12
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.32
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.02
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.52
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.01
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.52
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.74
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999988316
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.62
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000084184
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:17.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197885973.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27255
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.47
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.06
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.53
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.04
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.31
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.95
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.64
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.74
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.53
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.82
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.96
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5236.43
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908711
   j =  2                              :            45634
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908290
   j =  2                              :            45849
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.02
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.55
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.50
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.56
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.91
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.56
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.02
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.68
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.91
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.45
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.67
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.35
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.15
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.61
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.42
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.03
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.43
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.11
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.70
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.10
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.70
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.71
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.42
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.33
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.53
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.38
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.80
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.42
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.97
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.57
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.10
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.54
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.28
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.52
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.39
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.91
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.42
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.30
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.70
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9975
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.89
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.98
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.47
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9764.40
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10309.11
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.54
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.34
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.12
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.99
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.55
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.44
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.38
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999979013
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.22
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000145834
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:14.35
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199032853.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27256
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.97
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.41
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.16
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.86
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.07
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.99
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.29
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.84
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.59
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.00
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.27
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.46
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.41
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.33
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908405
   j =  2                              :            45793
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908269
   j =  2                              :            45861
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.01
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.05
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.12
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.38
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.54
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.84
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.53
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.68
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.41
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.88
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.70
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.30
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.90
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.75
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.77
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.30
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.82
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.85
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.97
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.82
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.60
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.00
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.31
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.43
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.64
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.74
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.83
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.44
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.75
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.01
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.23
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.12
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.83
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.62
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.02
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.94
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.99
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.46
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.95
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.23
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.72
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.22
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.44
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9758.39
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.55
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.00
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.60
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.30
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.07
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11474.52
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.59
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000089938
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.14
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000079840
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.019
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:35.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200048661.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27257
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 12                 :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.69
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.39
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.00
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.81
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.45
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.28
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.29
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.67
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.10
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 60                 :  9.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.78
 p-value of test no 61                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.57
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.80
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.81
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5195.82
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908556
   j =  2                              :            45719
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908074
   j =  2                              :            45960
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 79                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.27
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.87
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.06
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.84
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.37
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.09
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 140                :  1.0e-2
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   92.87
 p-value of test no 141                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.94
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.53
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.19
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.91
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.93
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.60
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.61
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.35
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.77
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.25
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.04
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.07
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.37
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.05
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.19
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.41
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.63
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.36
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.23
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.77
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.87
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.23
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.11
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.82
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.01
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.97
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.47
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.40
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.05
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.18
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.00
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.68
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.89
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.11
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.12
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.26
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.23
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.01
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.36
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.70
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.67
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.89
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.77
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000011929
 
 Normal statistic for number of bits   :   0.094
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.99
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999952262
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:54.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200966165.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27258
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.20
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.92
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.39
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.55
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.73
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.75
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.44
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.84
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.24
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.29
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.31
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.71
 p-value of test no 59                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.66
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.21
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.69
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.23
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5274.69
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908109
   j =  2                              :            45944
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908293
   j =  2                              :            45849
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
 p-value of test no 101                :    0.9980
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.71
 p-value of test no 118                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.13
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.24
 p-value of test no 120                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.93
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.26
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.54
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.27
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.02
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.46
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 143                :    0.9913
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17032.79
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.50
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.05
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.22
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.26
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.45
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.72
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.02
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.36
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.30
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.62
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.63
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.37
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.95
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.10
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.78
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.28
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.04
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.58
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.30
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.79
 p-value of test no 167                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.12
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.10
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.84
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.71
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.14
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.71
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.88
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.67
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.19
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.77
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.26
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.03
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.83
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.31
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.64
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.48
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5063.58
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.27
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.28
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.48
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.97
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.59
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000020467
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.71
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000029863
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:47.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201949205.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27259
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 9                  :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 10                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.23
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.45
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.65
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.01
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.38
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.56
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.75
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.31
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.95
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.30
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.15
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.51
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46087
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870087
   j =  1                              :        399907829
   j =  2                              :            46081
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908698
   j =  2                              :            45648
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.77
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.80
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.52
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.45
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.60
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.34
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.79
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.85
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.36
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.70
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.75
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.68
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.82
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.15
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.10
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.24
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.59
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.77
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.22
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.61
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.81
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.99
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.50
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.23
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.53
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.63
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.44
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.22
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.10
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.23
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.29
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.97
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.01
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.31
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.78
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.86
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.36
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.82
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   47.81
 p-value of test no 176                :  3.4e-6    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.04
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.49
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.03
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.70
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.68
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.17
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9729.39
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.76
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.68
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 223                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4672.02
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.39
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.66
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.09
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.78
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.93
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000033361
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.17
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000093583
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 253                :    0.9922
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:59.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9991 
  80  LinearComp, r = 0               3.4e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202899477.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27260
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 26                 :    0.9984
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     532
 p-value of test no 31                 :    0.9975
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.77
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.22
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.84
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.17
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.26
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.14
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.54
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.37
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.21
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6809.70
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.76
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.36
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.12
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.29
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907941
   j =  2                              :            46022
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908113
   j =  2                              :            45939
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
 p-value of test no 109                :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 111                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.055
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.77
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.41
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.93
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.52
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.03
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.76
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.35
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.98
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.77
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.10
 p-value of test no 134                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.17
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.38
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.70
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.49
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.95
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.27
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.90
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.60
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.36
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.72
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.02
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.36
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.87
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.14
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.91
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.80
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.55
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.06
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.01
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.66
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.34
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.51
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.18
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.99
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.46
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.72
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.24
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.84
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.13
 
 Sample variance                       :    2.15
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.84
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.73
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.71
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.57
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.35
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.48
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.51
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.73
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.73
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.82
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.50
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.81
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999930512
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.49
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999973541
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.64
 p-value of test no 238                :  4.2e-3
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:11.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183697430.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27261
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5233
 p-value of test no 13                 :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.32
 p-value of test no 41                 :  6.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.91
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.74
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.87
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.52
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.99
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.55
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.69
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.78
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.43
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.58
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.93
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907900
   j =  2                              :            46050
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907953
   j =  2                              :            46019
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.86
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.96
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.17
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.73
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.65
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.96
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.95
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.05
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.17
 p-value of test no 135                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.60
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17613.81
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.67
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.24
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.14
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.92
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.96
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.52
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.02
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.75
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.22
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.75
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.92
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.19
 p-value of test no 158                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.84
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.96
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.07
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.33
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.41
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.29
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.32
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.01
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.72
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.27
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.43
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.34
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.50
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.80
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.84
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.61
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.32
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.61
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.43
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.26
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.56
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.94
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.06
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.40
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.34
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.33
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.96
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.07
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.03
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000029656
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.31
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000017317
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    2.40
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:16.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184516630.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27262
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.67
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.07
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.03
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.43
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.83
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.02
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.31
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.64
 p-value of test no 59                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.74
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.87
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.97
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4915.36
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908844
   j =  2                              :            45569
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907742
   j =  2                              :            46123
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.84
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.51
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.79
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.59
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.66
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.15
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.44
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.21
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.05
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.86
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.01
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.15
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.68
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.46
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.45
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.00
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.27
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.91
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.64
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.13
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.83
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.46
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.20
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.76
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.95
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.65
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.54
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.71
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.63
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.74
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.01
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.12
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.37
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.90
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.35
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.27
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.35
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.73
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.10
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.19
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.23
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 214                :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.73
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.52
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.53
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.97
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.41
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.13
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11546.67
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.17
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000033943
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000087043
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    2.50
 p-value of test no 254                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:29.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185434134.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27263
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9934
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.28
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.12
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.09
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.89
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.41
 p-value of test no 51                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.76
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.41
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.38
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.98
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.56
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.76
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.66
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.12
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.48
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908342
   j =  2                              :            45820
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908619
   j =  2                              :            45686
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 102                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
 p-value of test no 109                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 111                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.76
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.39
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.28
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.13
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.33
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.52
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.00
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.64
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.83
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.48
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.70
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.02
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.21
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.65
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.14
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.16
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.06
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.70
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.72
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.88
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   98.16
 p-value of test no 159                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.57
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.20
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.74
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.04
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.69
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.54
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.80
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.20
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.91
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.40
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.34
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.51
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.70
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.51
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.25
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.19
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.98
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.94
 p-value of test no 177                :    0.9983
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    2.27
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.80
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.91
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.87
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.48
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.38
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.52
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.21
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4384.05
 p-value of test no 228                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.79
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.85
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.58
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000031915
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.17
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000059215
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:01.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186384406.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27264
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.58
 p-value of test no 29                 :  4.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    5.78
 p-value of test no 36                 :  1.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     362
 p-value of test no 37                 :  2.8e-4    *****
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.37
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.82
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.00
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.49
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.55
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.56
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.83
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.48
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.81
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.87
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.41
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908547
   j =  2                              :            45722
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46350
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870350
   j =  1                              :        399907302
   j =  2                              :            46346
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.64
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.06
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.81
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.29
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.65
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.62
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.57
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.69
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.76
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.11
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.09
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.90
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.59
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.43
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.36
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.84
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.28
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.86
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.50
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.74
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.90
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.11
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.45
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.75
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.24
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.39
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.91
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.73
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.90
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.95
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.94
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.97
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.11
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.04
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.06
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.78
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.96
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.70
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.99
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.41
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.82
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.83
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.57
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.78
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.47
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.11
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.47
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.98
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.97
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.88
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.52
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.87
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.10
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999978341
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.60
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000008002
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:05.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NJumps, t = 9        2.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187531286.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27265
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.85
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.94
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.55
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.58
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.69
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.38
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.14
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.60
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.29
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.03
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.62
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.81
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.07
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45570
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869570
   j =  1                              :        399908864
   j =  2                              :            45562
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908517
   j =  2                              :            45740
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 77                 :    0.9943
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 105                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.83
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.50
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.52
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.81
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.39
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.29
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.39
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.83
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.94
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.57
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.75
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.20
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.77
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.85
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.94
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.60
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.19
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.19
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.69
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.21
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.45
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.86
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.99
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.65
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.48
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.05
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.56
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.38
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.85
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.04
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.39
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.96
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.53
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.53
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.41
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.87
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.08
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.34
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.92
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.00
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.07
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.04
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.79
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.88
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.14
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.30
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.33
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.05
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999969539
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.57
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000023101
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:09.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188514326.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27266
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5290
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.85
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.97
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.25
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.55
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.24
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.74
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.90
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.74
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.05
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.11
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.06
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.14
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.71
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.58
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.20
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45322
 p-value of test no 70                 :    0.9954
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869322
   j =  1                              :        399909360
   j =  2                              :            45314
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908304
   j =  2                              :            45842
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.82
 p-value of test no 116                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.31
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.32
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.65
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.05
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.34
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.93
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.63
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.50
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.28
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.07
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.37
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.34
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.95
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.14
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.59
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.33
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.89
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.49
 p-value of test no 153                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.90
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.86
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.38
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.40
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.99
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.80
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.84
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.64
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.86
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.39
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.34
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.45
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.51
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.36
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.46
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.90
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.45
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.95
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.70
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.71
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.11
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.64
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.96
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.15
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.71
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.84
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.43
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.36
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9743.25
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.81
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.11
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.40
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.70
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.98
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.12
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.73
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999938702
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.39
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999921110
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:58.65
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189464598.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27267
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 6                  :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1197
 p-value of test no 11                 : 1 -  2.0e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334317
   j =  1                              :        599997606
   j =  2                              :             1197
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.02
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.74
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.14
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.19
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.18
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.86
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.56
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.17
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.68
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.72
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.54
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.83
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.43
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908552
   j =  2                              :            45721
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907875
   j =  2                              :            46058
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.68
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.74
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.95
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.42
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.70
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.58
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.12
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.84
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.59
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17488.39
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.34
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.28
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.00
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.34
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.00
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.56
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.40
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.32
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.39
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.71
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.23
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.26
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.84
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.40
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.65
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.27
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.66
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.72
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.36
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.59
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.35
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.72
 p-value of test no 170                :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.25
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.29
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.89
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.79
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.10
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.07
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.50
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.50
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.97
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.79
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.71
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.60
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.89
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.40
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.06
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.26
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000153070
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.38
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000061438
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:08.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  2.0e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190414870.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27268
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    3.23
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.91
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.94
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.32
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.88
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.63
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.71
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.46
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.83
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.74
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.57
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.63
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.62
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.10
 p-value of test no 66                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  157.29
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.47
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46108
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907785
   j =  2                              :            46106
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45667
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869667
   j =  1                              :        399908668
   j =  2                              :            45663
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  8.9e-3
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.30
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.69
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.94
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.06
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.55
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.94
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.62
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.35
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.36
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.61
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.23
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.55
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.14
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.34
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.41
 p-value of test no 152                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.44
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.91
 p-value of test no 156                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.81
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.85
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.22
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.93
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.90
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.38
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.75
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.21
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.86
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.63
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.04
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.09
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.42
 p-value of test no 170                :  5.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.29
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.37
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.32
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.91
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.33
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.86
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.23
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    2.28
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.43
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.84
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.49
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.64
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.85
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.66
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.19
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.57
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.07
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.54
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11529.68
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.30
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999913205
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.02
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000000172
 
 Normal statistic for number of bits   : 1.36e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:02.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191594518.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27269
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 12                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    5.22
 p-value of test no 36                 :  2.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.98
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.09
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.33
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.85
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.62
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.91
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1307.23
 p-value of test no 56                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.27
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.13
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.44
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.75
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4810.71
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908684
   j =  2                              :            45658
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908512
   j =  2                              :            45741
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9959
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.74
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.86
 p-value of test no 120                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.75
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.20
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.21
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.72
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.10
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.38
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.57
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.28
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.33
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.97
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.80
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.70
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.64
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.96
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.70
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.74
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.48
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.07
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.28
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.27
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.23
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.94
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.67
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.04
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.14
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.52
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.12
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.97
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.95
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.66
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.55
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.52
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.97
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.85
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.91
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.86
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.80
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.83
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.93
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.07
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.18
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.85
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.51
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.79
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.23
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.94
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.31
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11482.82
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.29
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000071629
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.64
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999887642
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:17.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192544790.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27270
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    3.79
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.07
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.00
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.25
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.78
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.22
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.15
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.47
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.86
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.59
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.31
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.70
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.25
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.40
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908248
   j =  2                              :            45870
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908080
   j =  2                              :            45954
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.84
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.29
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.77
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.08
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.17
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.15
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.39
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.60
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.01
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17788.47
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.30
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.36
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.46
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.33
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.99
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.04
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.25
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.12
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.94
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.08
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.11
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.66
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.99
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.98
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.32
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.38
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.01
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.80
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.68
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.76
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.76
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.37
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.62
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.63
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.99
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.47
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.79
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.18
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.90
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.74
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 181                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 182                :  7.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.43
 p-value of test no 183                :  7.5e-3
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 186                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.33
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.65
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.17
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.99
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.02
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.66
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.95
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.37
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.68
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.78
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.93
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.56
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000100900
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.66
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999810656
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.72e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:32.51
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193495062.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27271
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.57
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.25
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.14
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.80
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.91
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  366.13
 p-value of test no 55                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.78
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.66
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.94
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.19
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.01
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.14
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907769
   j =  2                              :            46114
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908620
   j =  2                              :            45684
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 115                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.83
 p-value of test no 117                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.53
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.36
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.40
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.33
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.54
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.29
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 132                :    0.9960
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.01
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.11
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17228.87
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.11
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.39
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.97
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.28
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.10
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.50
 p-value of test no 153                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.77
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.65
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.87
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.69
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.79
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.93
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.24
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.41
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.19
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.00
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.29
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.10
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.40
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.16
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.87
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.41
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.88
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.10
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.79
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.02
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.56
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.82
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.53
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.21
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.79
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.88
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.96
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.13
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.85
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.95
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.64
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.66
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000058891
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000136261
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.40
 p-value of test no 253                :  8.2e-3
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:27.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194412566.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27272
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7130
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.64
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.66
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.72
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.45
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.68
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.62
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.00
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.55
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7269.54
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.28
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.24
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.27
 p-value of test no 66                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.30
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.31
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907954
   j =  2                              :            46014
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908648
   j =  2                              :            45673
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.48
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.69
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.92
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.36
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 126                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.14
 p-value of test no 129                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.05
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.96
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.10
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.58
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.72
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.40
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.53
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.66
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.96
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.95
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.73
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.35
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.55
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.80
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.55
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.89
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.45
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.77
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.98
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4702.65
 p-value of test no 168                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.01
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.78
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.77
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.35
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.79
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.09
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.80
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.97
 p-value of test no 176                :  1.4e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.05
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.53
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
 p-value of test no 204                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  256.86
 p-value of test no 207                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.04
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.74
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.67
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.80
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.87
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.61
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.23
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.77
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.66
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000102973
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.15
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999944483
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:08.81
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195395606.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27273
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1487
 p-value of test no 9                  :  5.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334607
   j =  1                              :        599997026
   j =  2                              :             1487
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.58
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.35
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.36
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.25
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.27
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.61
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.52
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.04
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.97
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.04
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.96
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 58                 :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.75
 p-value of test no 59                 :  9.0e-4    *****
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 60                 :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.12
 p-value of test no 61                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.12
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.94
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.68
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.19
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907744
   j =  2                              :            46122
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908442
   j =  2                              :            45770
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 97                 :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.45
 p-value of test no 119                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.31
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.03
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.07
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.56
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.56
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.15
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.29
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.06
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.73
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.14
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.06
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.29
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.98
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.11
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.74
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.59
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.89
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.16
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.58
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.66
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.38
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.38
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.60
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.74
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.46
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.27
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.36
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.52
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.75
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.93
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.86
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.55
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.07
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.53
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.64
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-3
 p-value of test no 185                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 188                :  9.2e-3
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.49
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.23
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.98
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.24
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.59
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.41
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.78
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.87
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.33
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.33
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.86
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11561.84
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.15
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000005215
 
 Normal statistic for number of bits   :   0.041
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.86
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999924761
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:09.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196444182.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27274
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 5                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.94
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.01
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.46
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.96
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.15
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.94
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.08
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.00
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.07
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.57
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6915.81
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.04
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.91
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.75
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.99
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.83
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907836
   j =  2                              :            46079
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908613
   j =  2                              :            45689
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 115                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.73
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.20
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.59
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.86
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.99
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.31
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.13
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17110.10
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.73
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.37
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.40
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.73
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.35
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.67
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.65
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.48
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.98
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.52
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.09
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.18
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.58
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.79
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.21
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.68
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.62
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.76
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.88
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.91
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.57
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.80
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.17
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.74
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.18
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.35
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  471.11
 p-value of test no 172                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.94
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.87
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.54
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.13
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.31
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.58
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.24
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.10
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.16
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.46
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.36
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.28
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.89
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.10
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.14
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.84
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999989816
 
 Normal statistic for number of bits   :  -0.081
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.92
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000063967
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:54.84
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197656598.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27275
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.37
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.95
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.60
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.04
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.91
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.02
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.32
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.67
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.14
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.80
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.60
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-3
 p-value of test no 59                 :    0.9989
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.65
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.44
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.91
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.95
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.00
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46318
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870318
   j =  1                              :        399907370
   j =  2                              :            46306
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45579
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869579
   j =  1                              :        399908844
   j =  2                              :            45575
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.75
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.02
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.43
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.45
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.08
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.46
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.74
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.96
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.50
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.75
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.20
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.47
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.51
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.80
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.32
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.35
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.43
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.40
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.55
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.24
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.44
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.55
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.83
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.70
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.64
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.54
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.41
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.27
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.86
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.95
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.75
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.88
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.14
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.98
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.69
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.08
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.38
 p-value of test no 176                :    0.9986
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.94
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.80
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.16
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.98
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 204                :  8.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    5.17
 p-value of test no 206                :  2.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  144.18
 p-value of test no 207                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.28
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.93
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.17
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.42
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.73
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.04
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.28
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.87
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.18
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000048820
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.07
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999943397
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:38.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198606870.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27276
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.9914
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.63
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.42
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.56
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.44
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.18
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.20
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.45
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.95
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.35
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.91
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.01
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.27
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.69
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4847.49
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908313
   j =  2                              :            45839
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45564
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869564
   j =  1                              :        399908874
   j =  2                              :            45560
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
 p-value of test no 101                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.36
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.11
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.71
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.17
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.58
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.32
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.03
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.86
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.22
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.26
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.90
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.63
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.27
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.65
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.85
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.12
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.15
 p-value of test no 150                :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.30
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.46
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.33
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.00
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.72
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.18
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.34
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.40
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.59
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.10
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.42
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.85
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.70
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.50
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.23
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.44
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.05
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.81
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.84
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.53
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.50
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.12
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  298.82
 p-value of test no 174                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.19
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.08
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.86
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.64
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.13
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.05
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.43
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.88
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.68
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.75
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.31
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.99
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.95
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.90
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000200848
 
 Normal statistic for number of bits   :    1.59
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.21
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999808478
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9988
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:57.17
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199852054.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27277
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 6                  :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.14
 p-value of test no 33                 :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.17
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.15
 p-value of test no 49                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.54
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.01
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.10
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.71
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.47
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.88
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.45
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.29
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.37
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.55
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.13
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.16
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908368
   j =  2                              :            45804
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908567
   j =  2                              :            45712
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9947
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.39
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.46
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.50
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.28
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.84
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.96
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.29
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.56
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.16
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.54
 p-value of test no 136                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.67
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17033.29
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.74
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.10
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.50
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.72
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.96
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.93
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.11
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.27
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.61
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.61
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.65
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.45
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.48
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.07
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.93
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.61
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.12
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.25
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.60
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.49
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.51
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.28
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.79
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.45
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.07
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.98
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.52
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.96
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.52
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.41
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.93
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.94
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 223                :  1.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    9.02
 p-value of test no 225                :  4.3e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4508.41
 p-value of test no 226                : 1 -  3.8e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.21
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.24
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.89
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.15
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.59
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999934622
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.72
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999810125
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 251                :    0.9929
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.68
 p-value of test no 253                :    0.9963
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:26.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         0.9990 
  96  HammingIndep, L=30, r=27       1 -  3.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200835094.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27278
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4539
 p-value of test no 17                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    4.42
 p-value of test no 26                 :  5.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.97
 p-value of test no 40                 :  9.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.96
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.10
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.25
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.14
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.32
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.98
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.65
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.80
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.20
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.66
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.87
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908536
   j =  2                              :            45726
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908642
   j =  2                              :            45676
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.40
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.80
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.98
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.30
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.34
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.13
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.66
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.71
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.41
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.29
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.38
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.25
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.88
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.32
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.28
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.62
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.42
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.49
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.83
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.91
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.80
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.67
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.40
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.06
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.85
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.68
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.17
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.10
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.90
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.81
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.91
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.71
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.82
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.60
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.92
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.25
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.46
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.90
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.13
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.48
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.23
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.34
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.47
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.45
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.13
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 219                :  6.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 221                :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4620.59
 p-value of test no 222                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.57
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.39
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.65
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.38
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.84
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.46
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000017635
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.85
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000035239
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:41.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201850902.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27279
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5575
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    4.40
 p-value of test no 33                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.37
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.42
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.47
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.23
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.69
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.53
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.04
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.40
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.84
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.60
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.86
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.46
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.68
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908212
   j =  2                              :            45885
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907944
   j =  2                              :            46025
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 98                 :    0.9931
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 99                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.65
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  123.17
 p-value of test no 120                :  3.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.91
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.20
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.58
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.37
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.38
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.58
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
 p-value of test no 142                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17863.00
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.28
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.37
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.30
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.73
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.27
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.41
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.93
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.52
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.76
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.14
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.69
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.91
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.78
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.73
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.26
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.36
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.22
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.64
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.57
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.19
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.94
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.38
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.04
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.61
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.75
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4789.68
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.43
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.43
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.77
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.36
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.22
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.23
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.05
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.89
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.59
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.38
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.77
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.24
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.13
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.11
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.99
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.47
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000045244
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.62
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000085345
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:59:11.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           3.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202801174.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27280
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.72
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.58
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.48
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.18
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.11
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.56
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.12
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.70
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.06
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.71
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.98
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.86
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.40
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.60
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908126
   j =  2                              :            45937
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908207
   j =  2                              :            45895
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.22
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.84
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.77
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.51
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.30
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.55
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 127                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 128                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.07
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.78
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.92
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.04
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.74
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.07
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.90
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.34
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.83
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.10
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.00
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.51
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.58
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.92
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.39
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.32
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.11
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.25
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.79
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.21
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.29
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.64
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.56
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.54
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.60
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.38
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.93
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.69
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.78
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.34
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.84
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.83
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.04
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.41
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-4
 p-value of test no 193                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.96
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.45
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.97
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.48
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10236.93
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.91
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.55
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.60
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.80
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.60
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.99
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.30
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000008590
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.03
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999998789
 
 Normal statistic for number of bits   : -9.57e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:27.97
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183730199.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27281
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5603
 p-value of test no 13                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.21
 p-value of test no 34                 :  2.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.59
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.71
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.26
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.79
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.12
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.61
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.31
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.34
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.33
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.15
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.90
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.71
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.64
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.61
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908139
   j =  2                              :            45929
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908671
   j =  2                              :            45660
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.53
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.56
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.14
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.03
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.35
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.89
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.86
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.01
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.71
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.11
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.74
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.57
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.94
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.65
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.20
 p-value of test no 151                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.65
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.84
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.17
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.92
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.95
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.07
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.35
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.62
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.14
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.47
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.69
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.43
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.43
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.17
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.52
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.85
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.42
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.13
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.41
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.40
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.75
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.81
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.24
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.52
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.43
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.89
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.76
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.99
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.66
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.30
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.33
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.50
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.15
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.78
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.78
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000070231
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.07
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999980570
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:06.77
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184549399.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27282
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 10                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.73
 p-value of test no 35                 :  4.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.78
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.33
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.31
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.01
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.11
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.14
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.47
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.80
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6865.34
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.39
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.94
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.10
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.29
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.96
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907941
   j =  2                              :            46025
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907927
   j =  2                              :            46029
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 95                 :  8.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.14
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   35.44
 p-value of test no 120                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.39
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.14
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.81
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.80
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.53
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.61
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.58
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.33
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.54
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.86
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.85
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.68
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.01
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.38
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.52
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.41
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.66
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.56
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.83
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.10
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.82
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.56
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.16
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  209.33
 p-value of test no 164                :  5.4e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.40
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.27
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.81
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.52
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.16
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.03
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.43
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.22
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.11
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.19
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.53
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.79
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.90
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.80
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.94
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.88
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.32
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.85
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.80
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.57
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.51
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.18
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.09
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.10
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000098887
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.29
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999992135
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.95
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:30.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           0.9995 
  77  RandomWalk1 R (L=1000, r=20)    5.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185368599.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27283
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 9                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     821
 p-value of test no 25                 :    0.9960
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     537
 p-value of test no 31                 :    0.9952
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.69
 p-value of test no 35                 :  4.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.22
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.98
 p-value of test no 49                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.02
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.81
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.13
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.89
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.33
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.61
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.56
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.79
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.78
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.42
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.08
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908358
   j =  2                              :            45818
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908463
   j =  2                              :            45764
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
 p-value of test no 98                 :    0.9975
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 99                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.41
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.35
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.64
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.59
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.38
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.57
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.39
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.93
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17658.47
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.87
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.43
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.35
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.06
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.95
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.47
 p-value of test no 151                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.28
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.88
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.88
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.71
 p-value of test no 157                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.68
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.91
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.48
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.64
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.66
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.16
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.32
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.99
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.47
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.80
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.98
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.57
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.32
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.91
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.38
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.59
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.89
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.48
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.22
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.73
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.26
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.63
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.75
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.30
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.11
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3940.23
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.45
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12227.09
 p-value of test no 229                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.52
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000111430
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.19
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999931730
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.041
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:22.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186417175.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27284
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.18
 p-value of test no 22                 :  7.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.98
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.07
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.48
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.85
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.37
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.22
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.95
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.97
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.04
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.18
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.99
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.01
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.37
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.10
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5306.05
 p-value of test no 68                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907743
   j =  2                              :            46124
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907999
   j =  2                              :            45990
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 80                 :    0.9932
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9918
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.45
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.88
 p-value of test no 120                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.59
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.31
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.82
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.18
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.07
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.79
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.99
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.37
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.83
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.93
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.22
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.84
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.84
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.60
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.06
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.45
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.73
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.44
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.92
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.17
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.84
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.82
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.85
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.95
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.35
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.56
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.05
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.06
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.70
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.21
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.23
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.37
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.44
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.49
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.46
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.30
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.04
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.36
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.87
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.57
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.33
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.41
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.18
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.97
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.26
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.45
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999928328
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.57
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000044437
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 245                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 248                :    0.9923
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:45.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187367447.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27285
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 11                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.73
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.56
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.35
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.82
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.63
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.59
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.24
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.28
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6743.14
 p-value of test no 57                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.88
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.40
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.00
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.24
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908348
   j =  2                              :            45823
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908461
   j =  2                              :            45768
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 115                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.33
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.15
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.62
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.62
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.00
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.11
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.42
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.71
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.05
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.83
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.42
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.30
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.68
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.04
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.02
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.33
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.44
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.87
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.36
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.09
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.05
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.32
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.48
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.57
 p-value of test no 163                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.96
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.83
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.86
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.30
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.04
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.84
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.28
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.21
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.51
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.97
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.39
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.38
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.71
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.35
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.36
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.03
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.00
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.30
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.13
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.86
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.34
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.89
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.34
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.29
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.20
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000129070
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.98
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999836816
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:31.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188284951.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27286
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 6                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 8                  :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9900
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.13
 p-value of test no 47                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.08
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.80
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.56
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.99
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.10
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.16
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.58
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.17
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.05
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.50
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.06
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.16
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907884
   j =  2                              :            46049
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908250
   j =  2                              :            45872
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
 p-value of test no 98                 :    0.9932
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.16
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.17
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.22
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.17
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.98
 p-value of test no 123                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.84
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.57
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.41
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.37
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.98
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17459.37
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.77
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.24
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.80
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.82
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.42
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.47
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.91
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.28
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.11
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.71
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.65
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.71
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.84
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.68
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.43
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.70
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.62
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.57
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.67
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.93
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.21
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.76
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.07
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.41
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.77
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.27
 p-value of test no 176                :    0.9933
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.04
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.80
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.28
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.35
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.94e-4
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.81
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.63
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.19
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.89
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.70
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.69
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.72
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000053164
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.97
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999940100
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:06.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189366295.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27287
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.43
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.26
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.19
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.52
 p-value of test no 51                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.90
 p-value of test no 52                 :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.69
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.40
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.08
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.32
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.14
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.72
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.37
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.88
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.18
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908278
   j =  2                              :            45858
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908535
   j =  2                              :            45728
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-5
 p-value of test no 112                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.28
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.11
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.70
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.96
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.31
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.03
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.35
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.17
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.81
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.83
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.23
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.72
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.66
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.11
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.07
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.14
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.32
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.09
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.13
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.35
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.72
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.59
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.52
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.88
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.76
 p-value of test no 162                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.70
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.14
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.70
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.09
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.52
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.22
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.60
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.88
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.90
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.25
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.42
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.62
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.62
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.48
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.04
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.69
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.83
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.92
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.77
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.44
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.97
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.09
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.87
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.26
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.13
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.55
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000026485
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.98
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000114703
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:41.17
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190545943.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27288
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.06
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.78
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.10
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.15
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.63
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.11
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.96
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.40
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.03
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7080.89
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.84
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.27
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.85
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.48
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46108
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907787
   j =  2                              :            46102
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46209
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870209
   j =  1                              :        399907582
   j =  2                              :            46209
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.30
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.06
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.63
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.68
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.22
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.44
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.14
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.11
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.35
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.06
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.43
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.60
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.99
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.19
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.80
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.62
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.58
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.03
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.63
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.58
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.34
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.96
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.33
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.89
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.71
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.38
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.31
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.59
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.58
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.17
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.62
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.04
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.46
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.02
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.64
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.69
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.86
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.90
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.84
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.52
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.26
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 205                :  4.1e-4    *****
 
 Anderson-Darling statistic = A2       :    6.91
 p-value of test no 206                :  4.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  271.77
 p-value of test no 207                :  5.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.77
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.46
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.54
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.26
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.15
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.69
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.90
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.48
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.19
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999965000
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.31
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999901721
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:06.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        5.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191922199.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27289
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4506
 p-value of test no 16                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.43
 p-value of test no 28                 :  5.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    4.22
 p-value of test no 38                 :  6.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.93
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.58
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.35
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.81
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.79
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.22
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.34
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.03
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.23
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.02
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.03
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.86
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.44
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.27
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.01
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907964
   j =  2                              :            46009
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908612
   j =  2                              :            45688
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9944
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-4
 p-value of test no 110                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 111                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 117                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.35
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.11
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.13
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.74
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.77
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.84
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.37
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.78
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.41
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.68
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.68
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.73
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.55
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.05
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.48
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.51
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.43
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.98
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.16
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.00
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.20
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.37
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.42
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.58
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.04
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.43
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.24
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.16
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.08
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.01
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.98
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.24
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.71
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 191                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.94
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.59
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.62
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.69
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.48
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 217                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.39
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.53
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.62
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4278.37
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.01
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.50
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.90
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000080401
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.65
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999987605
 
 Normal statistic for number of bits   :  -0.098
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    2.38
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:37.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193101847.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27290
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.81
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    4.48
 p-value of test no 42                 :  5.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.39
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.29
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.25
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.70
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.89
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.10
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.47
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.15
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.93
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.10
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.19
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.10
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5117.66
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908276
   j =  2                              :            45856
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907936
   j =  2                              :            46029
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 73                 :    0.9936
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.52
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.14
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.09
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.07
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.40
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.71
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.17
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.38
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.22
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.91
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.08
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.57
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   66.42
 p-value of test no 147                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.76
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.38
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.42
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.26
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.23
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.66
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.18
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.54
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.10
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.74
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.71
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.32
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.67
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.26
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.51
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.49
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.50
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.53
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5224.00
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.38
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.93
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.26
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.13
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.96
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.82
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.43
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.62
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 180                :  5.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    7.67
 p-value of test no 182                :  1.8e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.76
 p-value of test no 183                : 1 -  8.5e-5    *****
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.63
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.08
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.58
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.09
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.28
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.65
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.66
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.17
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.88
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.39
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.71
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000182572
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.95
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000085516
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:17.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  82  LempelZiv, r = 0               1 -  8.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194117655.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27291
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1237
 p-value of test no 9                  :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334357
   j =  1                              :        599997526
   j =  2                              :             1237
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5568
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.76
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.63
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.65
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.74
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.12
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.12
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  284.68
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.28
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.67
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7335.14
 p-value of test no 57                 :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.30
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.07
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.95
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.34
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908251
   j =  2                              :            45870
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908552
   j =  2                              :            45718
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.96
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.43
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.81
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.96
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.57
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.51
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.03
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.51
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.11
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.51
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17693.81
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.86
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.99
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.30
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.58
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.72
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.40
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.34
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.75
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.66
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.08
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.69
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.42
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.50
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.81
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.87
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.25
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.14
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.43
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.89
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.42
 p-value of test no 167                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.86
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.43
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.39
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.71
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.06
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.08
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.06
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.60
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.18
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.04
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.09
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.65
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.02
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.07
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.64
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.39
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.00
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.10
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12068.89
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.36
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999992471
 
 Normal statistic for number of bits   :  -0.060
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.49
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999959204
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    2.05
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:32.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195133463.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27292
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7096
 p-value of test no 20                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.46
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.65
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.25
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.91
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.35
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.92
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.83
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.03
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.72
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6822.10
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.26
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.77
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.81
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46185
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907632
   j =  2                              :            46181
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907825
   j =  2                              :            46077
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.75
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.25
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.40
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.06
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.99
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.36
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.20
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.73
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.81
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.75
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17417.92
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.49
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.01
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.13
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.26
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.55
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.78
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.90
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.64
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.03
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.97
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.88
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.42
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.30
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.55
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.96
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.45
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.43
 p-value of test no 165                :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.67
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.09
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.97
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.05
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.41
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.04
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.37
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.96
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.04
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.32
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.69
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 181                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.92
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.39
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.00
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.92
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.88
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.07
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.39
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.17
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.43
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.30
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.86
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.32
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000147676
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.56
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000112648
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:40.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196149271.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27293
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.90
 p-value of test no 22                 :  1.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.17
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.02
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.80
 p-value of test no 51                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.92
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.46
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  177.99
 p-value of test no 54                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.09
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.34
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.58
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.79
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.79
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.07
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.40
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4890.62
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907965
   j =  2                              :            46013
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908364
   j =  2                              :            45815
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-5
 p-value of test no 112                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-4
 p-value of test no 113                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 114                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.79
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.73
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.08
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.80
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.02
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.25
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.99
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.65
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.33
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.32
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.41
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.62
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.70
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.86
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.80
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.17
 p-value of test no 152                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.82
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.25
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.81
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.20
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.78
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.37
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.44
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.64
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.72
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.07
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.78
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.99
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.36
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.83
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.11
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.11
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.10
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.86
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.80
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.69
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.68
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.80
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.09
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    2.46
 p-value of test no 189                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.92
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.43
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.14
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.59
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.86
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.73
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.72
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.16
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.16
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.89
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11440.25
 p-value of test no 230                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.03
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999811259
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.72
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000011959
 
 Normal statistic for number of bits   :   0.095
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:20.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197165079.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27294
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5304
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    4.42
 p-value of test no 24                 :  5.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    6.32
 p-value of test no 26                 :  7.1e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.61
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.72
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.96
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.06
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.64
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.49
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.04
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.07
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.60
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.87
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.56
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.19
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.09
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.15
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5186.70
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45557
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869557
   j =  1                              :        399908887
   j =  2                              :            45555
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45636
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908733
   j =  2                              :            45626
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.85
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.82
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.08
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.49
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.84
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.30
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.74
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.02
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.10
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.20
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17255.05
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.80
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.74
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.67
 p-value of test no 149                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.59
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.54
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.01
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.17
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.87
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.91
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.37
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.34
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.51
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.70
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.92
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.36
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.51
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.32
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.78
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.21
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.15
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.73
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.97
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.91
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.70
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.42
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.76
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.55
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.02
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.54
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.62e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.77
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.01
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.55
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.32
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.90
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4690.82
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.07
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.54
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.92
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.75
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.71
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000106372
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.91
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999901313
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.078
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.96
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:51.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          7.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198115351.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27295
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9943
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.32
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.82
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.09
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.19
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.38
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.61
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.56
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.47
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.68
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.57
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.73
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.79
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.98
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.48
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907983
   j =  2                              :            46004
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907882
   j =  2                              :            46053
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.08
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.19
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.93
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.82
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.22
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.05
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.38
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.47
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17241.52
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.91
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.26
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.26
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.94
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.15
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.47
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.12
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.16
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.95
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.13
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.79
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.79
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.48
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.96
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.42
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.08
 p-value of test no 166                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.44
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.52
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.83
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.14
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.63
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.37
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.92
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.93
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.33
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.85
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.60
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.80
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.48
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9766.23
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.32
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.19
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.94
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.51
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.55
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12211.44
 p-value of test no 230                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.58
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000112141
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.39
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000050065
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:22.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199131159.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27296
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1232
 p-value of test no 11                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334352
   j =  1                              :        599997536
   j =  2                              :             1232
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.70
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.52
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.36
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.84
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.09
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.85
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.03
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.30
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.90
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.35
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.37
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.02
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908110
   j =  2                              :            45942
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908186
   j =  2                              :            45904
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.66
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.74
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.10
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.36
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.13
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.69
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.00
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.50
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.97
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.38
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.14
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.59
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.74
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.91
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.68
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.01
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.52
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   40.01
 p-value of test no 155                :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.70
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.18
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.49
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.81
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.25
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.64
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.62
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.09
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.68
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.47
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.25
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.17
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.51
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.32
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.92
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.86
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.66
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.31
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.14
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.80
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.45
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.85
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.74
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 183                :    0.97
 
 Sample variance                       :    2.26
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.87
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.54
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 204                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.03
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.61
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.85
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.79
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.32
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.51
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.59
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12153.25
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.55
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.92
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000112519
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.22
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000122824
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.42e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:19.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200146967.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27297
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4496
 p-value of test no 14                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.95
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.37
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.06
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.37
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.86
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.56
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.86
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.98
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.83
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.49
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.62
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.34
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.85
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.82
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908368
   j =  2                              :            45807
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908421
   j =  2                              :            45788
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.72
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.96
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.02
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.21
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.77
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.75
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.32
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.30
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.68
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.97
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.87
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.16
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.01
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.35
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.05
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.71
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.98
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.28
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.87
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.08
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.65
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.42
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.21
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.41
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.28
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.34
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.17
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.43
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  581.22
 p-value of test no 163                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.39
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.64
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.76
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.29
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.08
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.56
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.74
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.15
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.20
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4793.75
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.98
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.51
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.63
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.78
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    2.06
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.49
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.76
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.30
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.91
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.72
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.25
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.74
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.35
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.27
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.01
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.26
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.93
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000068299
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.52
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999944957
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.97
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:38.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201097239.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27298
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7135
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.57
 p-value of test no 47                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.88
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.21
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.58
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.05
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.36
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.50
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.46
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.99
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.58
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.47
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.47
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.68
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907915
   j =  2                              :            46038
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46315
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870315
   j =  1                              :        399907373
   j =  2                              :            46309
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.35
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.43
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.49
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.16
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.32
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.37
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.54
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.53
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17601.12
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.91
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.40
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.68
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.63
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.84
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.81
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.24
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.80
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.13
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.75
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.12
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.81
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.17
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.86
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.35
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.76
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.78
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.02
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.67
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.24
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.41
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.93
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.20
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.82
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  295.88
 p-value of test no 174                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.80
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.33
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.01
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.19
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.42
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.75
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.25
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.08
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.94
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.59
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.88
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.50
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.22
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000077518
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.16
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999847307
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:23.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               0.9991 
  79  RandomWalk1 R (L=10000, r=15)   0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202178583.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27299
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 10                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.97
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.59
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.57
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.96
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.85
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.87
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.81
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6993.88
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.37
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.63
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.73
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.21
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45617
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869617
   j =  1                              :        399908769
   j =  2                              :            45611
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908319
   j =  2                              :            45836
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.05
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.09
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.25
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.26
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.10
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.34
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.87
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.95
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.34
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.44
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.07
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.26
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.97
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.72
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.97
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.61
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.06
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.40
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.91
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.20
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.19
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.01
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.87
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.47
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.78
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.18
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.32
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.87
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.85
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.56
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.56
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.61
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.93
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.27
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.17
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.43
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.14
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.66
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.40
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.71
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.44
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.54
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10257.90
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.16
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.66
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.08
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.23
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.03
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.07
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.05
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.73
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999872663
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.49
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999930272
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:57:55.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203161623.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27300
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.11
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.90
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.62
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.15
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.46
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.83
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.45
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.66
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.34
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.17
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.46
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.48
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.90
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.43
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.73
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46242
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870242
   j =  1                              :        399907521
   j =  2                              :            46232
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908373
   j =  2                              :            45812
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 103                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 104                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    6.81
 p-value of test no 105                :  4.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-6
 p-value of test no 109                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.28
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.85
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.74
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.51
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.68
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.27
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.79
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.96
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.34
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.26
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.83
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.55
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.33
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.50
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.70
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.33
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.70
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.30
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.92
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.48
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.01
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.93
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.36
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.03
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.66
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.53
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.20
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.54
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.45
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.13
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.94
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.99
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.71
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.05
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.24
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.25
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.32
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.31
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.93
 p-value of test no 177                :    0.9983
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.73
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.67
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.32
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.90
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.69
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.83
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.95
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.07
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.38
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.88
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.00
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.64
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.29
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000048427
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.99
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999941912
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :  1.0e-2
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:29.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  51  SampleProd, t = 16              4.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183762968.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27301
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5266
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.96
 p-value of test no 48                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.32
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.81
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.03
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.01
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.49
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.43
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1556.11
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.31
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.99
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.03
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5246.29
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908287
   j =  2                              :            45852
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908074
   j =  2                              :            45960
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.27
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.39
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.55
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.99
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.30
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.04
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.86
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.81
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.60
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17263.25
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.73
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.08
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.85
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.27
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.48
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.61
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.86
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.42
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.11
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.49
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.89
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.17
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.77
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.37
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.89
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.25
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.00
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.15
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.68
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.58
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.03
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.68
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.96
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.43
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.11
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.19
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.88
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.16
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.20
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.13
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.27
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 181                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.11
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.46
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.19
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.94
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.82
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.03
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.52
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.49
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.41
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.18
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.96
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999917168
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.41
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000033079
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:28.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184156184.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27302
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.68
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.86
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.33
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.61
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.49
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.09
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.52
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.33
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.94
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.63
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.92
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.49
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908522
   j =  2                              :            45736
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908203
   j =  2                              :            45897
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.20
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.93
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.65
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.32
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.41
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.11
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.42
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.52
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.66
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.84
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.34
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.36
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.86
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.19
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.12
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.93
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.76
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.75
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.08
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.11
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.09
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.16
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.89
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.08
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.90
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.62
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.98
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.61
 p-value of test no 165                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.44
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.78
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.03
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.92
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.96
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.36
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.73
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.15
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.49
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.38
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.89
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.80
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.42
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.01
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.36
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.28
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.47
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.87
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.01
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.00
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.20
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.82
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.27
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.67
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999998918
 
 Normal statistic for number of bits   : -8.55e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.40
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999896012
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:08.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185040920.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27303
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 4                  :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.17
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.21
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.88
 p-value of test no 49                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.00
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.34
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.55
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.62
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.03
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.32
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.41
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.46
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.94
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.48
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.79
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.89
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.08
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908306
   j =  2                              :            45841
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907898
   j =  2                              :            46042
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.11
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.59
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.39
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.00
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.63
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.31
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.83
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.64
 p-value of test no 134                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.46
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.30
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.79
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.41
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.61
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.45
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.87
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.03
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.54
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.69
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.73
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.75
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.11
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.56
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.18
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.87
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.77
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.51
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.80
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.41
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.17
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.68
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.96
 p-value of test no 167                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.86
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.46
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.10
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.93
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.43
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.03
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.45
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.89
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.07
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.53
 p-value of test no 178                :  4.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.34
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.71
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.35
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10324.06
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.05
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.07
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.92
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.11
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.26
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.52
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11511.81
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.78
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000143077
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.08
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000182770
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.020
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:36.81
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186089496.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27304
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.87
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.92
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.93
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.71
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.14
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.58
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.03
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.91
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.19
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.30
 p-value of test no 65                 :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.33
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.87
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908382
   j =  2                              :            45803
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45612
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869612
   j =  1                              :        399908780
   j =  2                              :            45604
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.96
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.49
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.13
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.20
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.37
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.70
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.47
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.60
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.07
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17490.16
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.17
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.95
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.81
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.04
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.76
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.85
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.86
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.45
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.69
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.92
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.99
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.57
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.53
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.62
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.50
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.38
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.86
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.80
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.46
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.52
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.70
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.26
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.97
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.17
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.92
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.40
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.85
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.59
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.77
 p-value of test no 175                :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.31
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.77
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.37
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 210                :    0.9972
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.77
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.60
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 220                :  4.3e-4    *****
 
 Anderson-Darling statistic = A2       :    6.19
 p-value of test no 221                :  8.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5192.22
 p-value of test no 222                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.06
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.83
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.41
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.65
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.81
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.50
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999706139
 
 Normal statistic for number of bits   :   -2.32
 p-value of test no 232                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.20
 p-value of test no 233                :  8.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999870503
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.023
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:28.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187072536.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27305
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.15
 p-value of test no 49                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.52
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.14
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.50
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.45
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.94
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.81
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.58
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.98
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.09
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.04
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.92
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.29
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908156
   j =  2                              :            45922
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908836
   j =  2                              :            45573
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.80
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.46
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.26
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.46
 p-value of test no 123                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.04
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.23
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.92
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.86
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.90
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.13
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.74
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.44
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.62
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.20
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.36
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.12
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.32
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.04
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.11
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.58
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.84
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.55
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.13
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.95
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.30
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.92
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.54
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.04
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.91
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.89
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.82
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.02
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.48
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.71
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.64
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.38
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.96
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.47
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 187                :    0.9998    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.04
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.04
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.74
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.01
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9697.77
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.71
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.66
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.71
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.39
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11562.20
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12217.14
 p-value of test no 230                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.29
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999878162
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.44
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999760904
 
 Normal statistic for number of bits   :   -1.89
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    2.30
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:57.67
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188055576.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27306
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997247
   j =  2                              :             1375
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 7                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.43
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.66
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.71
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.69
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.00
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.45
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.61
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.44
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.41
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.84
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.43
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.59
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.33
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.77
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.42
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907929
   j =  2                              :            46028
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907798
   j =  2                              :            46098
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9937
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.51
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.16
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.96
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.30
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.63
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.11
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.40
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.02
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.40
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.10
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17325.93
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.81
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.13
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.79
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.39
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.74
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.96
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.81
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.97
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.62
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.26
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.95
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.94
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.72
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.33
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.87
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.44
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.58
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.28
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.04
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.18
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.92
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.53
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.29
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.25
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.74
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.66
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.43
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.63
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.74
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.05
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.09
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    2.63
 p-value of test no 184                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.44
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.95
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.53
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.82
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.18
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.62
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.74
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.41
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.41
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.36
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.91
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000196279
 
 Normal statistic for number of bits   :    1.55
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.33
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999971747
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.26e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.38
 p-value of test no 253                :  8.6e-3
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:18.07
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189104152.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27307
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.82
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.63
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.27
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.50
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.12
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.14
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.41
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.30
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.89
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.23
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.47
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.36
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908456
   j =  2                              :            45766
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908454
   j =  2                              :            45770
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.66
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.90
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.50
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.30
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.30
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.37
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.05
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.48
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.66
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.92
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17776.39
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.29
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.47
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.35
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.69
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.65
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.44
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.77
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.66
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.31
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.80
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.61
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.72
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.74
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.69
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.59
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.80
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.03
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.29
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.62
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.04
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.68
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.39
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.87
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.15
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.76
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.62
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.39
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.07
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.99
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.99
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.43
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.49
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.65
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.09
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.35
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.89
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.74
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.46
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.32
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.77
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999944816
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.58
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999979343
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:12.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190087192.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27308
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 32                 :    0.9990    *****
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.30
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.92
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.59
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.45
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.77
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.28
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.74
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.28
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.78
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.13
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.09
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.80
 p-value of test no 58                 :  3.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 60                 :  5.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.61
 p-value of test no 61                 :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.94
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.39
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.88
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907863
   j =  2                              :            46061
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908895
   j =  2                              :            45548
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 102                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.16
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.38
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.89
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.01
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.19
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.86
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.50
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.17
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.90
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17207.33
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.58
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.15
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.19
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.51
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.71
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.85
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.68
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.29
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.46
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.95
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.25
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.96
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.93
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.44
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.68
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.89
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.43
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.74
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.33
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.63
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.38
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.74
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.94
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.77
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.03
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.16
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.68
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.84
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.62
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.69
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.85
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.97
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.12
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.48
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.95
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.83
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.68
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.97
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.03
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.07
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.00
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.73
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.55
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999971687
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.44
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000023476
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:23.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191103000.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27309
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.70
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.01
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.43
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.72
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.19
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.89
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.78
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.75
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.68
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6874.80
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.08
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.61
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.82
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.97
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.72
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908038
   j =  2                              :            45975
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908208
   j =  2                              :            45890
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.62e-4
 p-value of test no 110                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 111                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.28
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.14
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.34
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.25
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.55
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.37
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.88
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.45
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.71
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.66
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.54
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.78
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.67
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.95
 p-value of test no 149                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.48
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.74
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.90
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.86
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.05
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.02
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.84
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.51
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.17
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.11
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.64
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.01
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.66
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.79
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.21
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.51
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.37
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.70
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.01
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.36
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.59
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.52
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.73
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.34
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.53
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.37
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.37
 p-value of test no 176                :    0.9986
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.57
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 183                :    0.04
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.36
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.26
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.70
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.51
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.43
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.68
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.66
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.41
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.39
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.27
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.76
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.71
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000103684
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.67
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999975620
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:07.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192184344.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27310
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 11                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4490
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.69
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.75
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.18
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.40
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.86
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.22
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.18
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  377.82
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.45
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.64
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.80
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.66
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.03
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.79
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4828.19
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908531
   j =  2                              :            45730
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908270
   j =  2                              :            45865
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 80                 :    0.9925
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.51
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.36
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.84
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.31
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.95
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.45
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.53
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.48
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.47
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.92
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17426.85
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.70
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.83
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.21
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.73
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.97
 p-value of test no 151                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.84
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.38
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.73
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.97
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.27
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.12
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.73
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.30
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.88
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.42
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.42
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.55
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.54
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.87
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.09
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.76
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.74
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.97
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.09
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.95
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.22
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.62
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.10
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.80
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.90
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.83
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.52
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.37
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.98
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.86
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.39
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3922.24
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.85
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.48
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.34
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.37
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000125515
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.29
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999994871
 
 Normal statistic for number of bits   :  -0.041
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:17.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193167384.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27311
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.18
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.64
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.27
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.37
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.38
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.15
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.91
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.35
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.19
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.05
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.41
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.96
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.03
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.74
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907749
   j =  2                              :            46118
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907879
   j =  2                              :            46059
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 77                 :  9.7e-4    *****
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 78                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 103                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 105                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.80
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.96
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.12
 p-value of test no 121                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.12
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.34
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.19
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.87
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.51
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.42
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.38
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17072.22
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.57
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.89
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.42
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.28
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.02
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.60
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.60
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.81
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.48
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.09
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.00
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.26
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.28
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.47
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.43
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.51
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.45
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.45
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.35
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.66
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.83
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.58
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.24
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.32
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.97
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.24
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.62
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.16
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.48
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.09
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.30
 p-value of test no 198                :  9.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.49
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.43
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.41
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.31
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.51
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.19
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.05
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.18
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.93
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12086.71
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.53
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999918338
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.48
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000121876
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 236                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    2.41
 p-value of test no 244                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:58.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194150424.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27312
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.93
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.81
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.47
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.63
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.78
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.81
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  375.64
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.87
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.12
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.54
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.80
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.02
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.12
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4807.77
 p-value of test no 68                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908254
   j =  2                              :            45864
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908064
   j =  2                              :            45965
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 101                :    0.9946
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.87
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.95
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.19
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.19
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.31
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.48
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.08
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.38
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.96
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.05
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17357.88
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.10
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.54
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.78
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.83
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.27
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.08
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.98
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.89
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.32
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.20
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.02
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.03
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.73
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.54
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.88
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.39
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.56
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.21
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.69
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.08
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.04
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.71
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.69
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.52
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.54
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.47
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.82
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.19
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.42
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.86
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.53
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5065.33
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.54
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.08
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.97
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.81
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.22
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.00
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000050710
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.75
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000098554
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:03.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195166232.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27313
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5573
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.68
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.55
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.76
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.95
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.76
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.43
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.53
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.96
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.06
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.79
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.76
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.07
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.27
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.14
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.35
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.34
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908145
   j =  2                              :            45923
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908155
   j =  2                              :            45918
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 94                 :    0.9908
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.91
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.99
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.99
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.02
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.95
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.08
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.14
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.27
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.11
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.99
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.07
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.78
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.37
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.90
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.52
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.22
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.71
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.63
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.08
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.58
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.42
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.12
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.34
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.23
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.97
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.66
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.79
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.63
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.85
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.43
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.37
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.52
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.48
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.41
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.00
 p-value of test no 175                :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.05
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.20
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.83
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.12
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.46
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.45
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.51
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.74
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.74
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.19
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.12
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999985205
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.02
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999968717
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:16.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196182040.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27314
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.67
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.82
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.30
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.27
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.24
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.35
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  486.67
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.92
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.72
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.31
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.37
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.55
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.37
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.87
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45334
 p-value of test no 70                 :    0.9946
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869334
   j =  1                              :        399909334
   j =  2                              :            45330
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908298
   j =  2                              :            45848
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.00
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.16
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.95
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.20
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.36
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.20
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.92
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.40
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.77
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.13
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17555.75
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.83
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.46
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.35
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.37
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.34
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.87
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.65
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.96
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.77
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.49
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.39
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.73
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.74
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.42
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.98
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.05
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.89
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.79
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.65
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.24
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.11
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.93
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.26
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.60
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.73
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.44
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.99
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.55
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.35
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.20
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.50
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.22
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.90
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.60
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.69e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.10
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5062.46
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.79
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.64
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.79
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.01
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.90
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000102229
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999905165
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:42.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197197848.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27315
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.44
 p-value of test no 34                 :  5.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    3.27
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.50
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.34
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.28
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.16
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.85
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.77
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.65
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.22
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.48
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.11
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.71
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.34
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.09
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.97
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.72
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908208
   j =  2                              :            45887
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908289
   j =  2                              :            45851
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  7.5e-3
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.39
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.35
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.80
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.11
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.83
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.77
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.74
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   17.28
 p-value of test no 135                :  6.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.80
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17818.74
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.93
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.30
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.87
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.09
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.52
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.60
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.82
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.21
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.80
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.58
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.76
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.46
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.24
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.09
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.87
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.71
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.86
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.76
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.83
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.38
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.31
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.42
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.08
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  150.36
 p-value of test no 170                :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.00
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.46
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.32
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.58
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.78
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.52
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.83
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.93
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.75
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.34
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.40
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.11
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.89
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.39
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.02
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.80
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.66
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000017971
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.37
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000066367
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:37.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198213656.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27316
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.40
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.53
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.18
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  180.75
 p-value of test no 54                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.42
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.62
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6927.60
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.05
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.90
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.51
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.38
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908128
   j =  2                              :            45924
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908057
   j =  2                              :            45967
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 73                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.38
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.03
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.76
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.31
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.17
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.34
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.77
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.06
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.79
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.58
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 144                :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17930.93
 p-value of test no 145                :  3.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.45
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.35
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.13
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.00
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.44
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.41
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.98
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.01
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.22
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.22
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.19
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.72
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.74
 p-value of test no 159                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.14
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.84
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.40
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.66
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.42
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.67
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.67
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.31
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4766.75
 p-value of test no 168                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.56
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.78
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.64
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.11
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.98
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.86
 p-value of test no 174                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.44
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.30
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.97
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.01
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.70
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9972
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.84
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5058.69
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.86
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.52
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.03
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.00
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.01
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.55
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000001378
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.31
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000236728
 
 Normal statistic for number of bits   :    1.87
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:48.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199229464.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27317
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 11                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.61
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.13
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.29
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.79
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.29
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.90
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.82
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.63
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.41
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.11
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.01
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.81
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.27
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908350
   j =  2                              :            45819
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908735
   j =  2                              :            45628
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.43
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.10
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.32
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.67
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.62
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.64
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.96
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.23
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.34
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17598.62
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.03
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.52
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.50
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.23
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.26
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.83
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.59
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.50
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.49
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.82
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.53
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.15
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.81
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.82
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.95
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  582.58
 p-value of test no 163                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.31
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.17
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.75
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.65
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.45
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.83
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.02
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.00
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.56
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.21
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.53
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.21
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.35
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.51
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.13
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.40
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.78
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.83
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.97
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.98
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.58
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.59
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.70
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.11
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.15
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.64
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999928529
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.90
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000118354
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 248                :    0.9932
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:43.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200278040.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27318
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 3                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.29
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    4.10
 p-value of test no 44                 :  7.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.95
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.83
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.58
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.40
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.68
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.69
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.34
 p-value of test no 52                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.69
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.80
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.56
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.80
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.81
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.14
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.71
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.38
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.62
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908191
   j =  2                              :            45903
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45507
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869507
   j =  1                              :        399908989
   j =  2                              :            45501
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.18
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.83
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.44
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.69
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.81
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.76
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.90
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.09
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.85
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.13
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.87
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.35
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.53
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.10
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.52
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.05
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.39
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.39
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.00
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.71
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.16
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.36
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.95
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.60
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.84
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.35
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.56
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.88
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.38
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.52
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.47
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.07
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.60
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.67
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.52
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.24
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.08
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.15
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.46
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.66
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.86
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.72
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.77
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 219                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.37
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.96
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.92
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.32
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.05
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.80
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.77
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999971765
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.40
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999981314
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    2.20
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:21.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201261080.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27319
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.44
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.79
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.92
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.47
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.55
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.25
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.96
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.20
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.46
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.91
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.47
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.41
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.94
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.16
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908190
   j =  2                              :            45902
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908696
   j =  2                              :            45643
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.29
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.70
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.64
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.81
 p-value of test no 124                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.39
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.89
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.85
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.04
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.95
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.91
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.33
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.93
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.61
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.78
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.16
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.54
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.24
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.22
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.87
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.13
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.15
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.25
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.74
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.31
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.78
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.41
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.83
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.06
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.88
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.89
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.32
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.53
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.13
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.55
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.68
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.30
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5258.62
 p-value of test no 173                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.96
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.77
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.93
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.15
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.16
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.28
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.17
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.31
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.29
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.82
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.52
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.54
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.71
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11590.39
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.23
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999991043
 
 Normal statistic for number of bits   :  -0.071
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.94
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000008995
 
 Normal statistic for number of bits   :   0.071
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
 p-value of test no 250                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:40.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202342424.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27320
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9924
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.46
 p-value of test no 46                 :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.94
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.18
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.05
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.29
 p-value of test no 52                 :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.11
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.73
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.57
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1560.49
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.03
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.05
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.37
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.58
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.13
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46197
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907607
   j =  2                              :            46195
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908399
   j =  2                              :            45799
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.22
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.61
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.34
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.66
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.39
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.76
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.14
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.83
 p-value of test no 129                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.05
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.00
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.74
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.75
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.17
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.49
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.22
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.58
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.13
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.04
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.13
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.22
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.87
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.68
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.43
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.46
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.67
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.69
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.78
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.68
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.83
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.53
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.02
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.58
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5240.39
 p-value of test no 168                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.40
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.28
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.54
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.62
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.53
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.05
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.37
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.89
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.95
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.99
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.62
 p-value of test no 203                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.32
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.46
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.90
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.06
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.82
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.91
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.13
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.15
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.39
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.72
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000142012
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.03
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000021202
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.62e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    3.07
 p-value of test no 254                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:21:57.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183795737.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27321
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    3.43
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     526
 p-value of test no 31                 :    0.9989
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.40
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.20
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.95
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.25
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.72
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.49
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.34
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.72
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.28
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.44
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.49
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.84
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46381
 p-value of test no 70                 :  9.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870381
   j =  1                              :        399907240
   j =  2                              :            46377
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908464
   j =  2                              :            45765
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.30
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.99
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.52
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.95
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.17
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.48
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.62
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.24
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.34
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.72
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.08
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.53
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.06
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.89
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.36
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.09
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.73
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.27
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.49
 p-value of test no 154                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.98
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.70
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.67
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.51
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.47
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.58
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.25
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.78
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.50
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.34
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.69
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.76
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.70
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.65
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.91
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.34
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.38
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.18
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.43
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.97
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.89
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.05
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.74
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.84
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.66
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.80
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.43
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.96
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3966.63
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.04
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.99
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.89
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000139582
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.90
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999993020
 
 Normal statistic for number of bits   :  -0.055
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:57.67
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184844313.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27322
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.22
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.50
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.01
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.65
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.93
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.73
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.39
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.87
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.82
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.79
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  8.9e-3
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.98
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.01
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.36
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.45
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908438
   j =  2                              :            45775
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908270
   j =  2                              :            45862
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-4
 p-value of test no 110                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.85
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.85
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.12
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.32
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.97
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.74
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.44
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.64
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.12
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17620.97
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.43
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.41
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.63
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.65
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.72
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.67
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.87
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.72
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.99
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.89
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.81
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.18
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.53
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.68
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.21
 p-value of test no 160                :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.52
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.17
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.55
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.37
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.27
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.64
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.72
 p-value of test no 167                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.14
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.05
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.81
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.74
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.29
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.12
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.26
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.21
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.45
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.51
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.98
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.13
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.15
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.42
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.39
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4720.51
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.01
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.74
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.39
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11449.33
 p-value of test no 230                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.60
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000031867
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.40
 p-value of test no 233                :    0.9913
 
 
 -----------------------------------------------
 Total number of bits:  8000129751
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    2.17
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:20.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185892889.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27323
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 12                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.33
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.75
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.94
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.39
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.12
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.71
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.56
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.88
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.38
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6911.80
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.01
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.28
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.82
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.54
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.95
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46111
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870111
   j =  1                              :        399907779
   j =  2                              :            46109
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907798
   j =  2                              :            46095
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-3
 p-value of test no 84                 :    0.9981
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.81
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.91
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.81
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.06
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.75
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.28
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.94
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.21
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.35
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.40
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.88
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.55
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.58
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.69
 p-value of test no 150                :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.70
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.13
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.67
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   98.84
 p-value of test no 156                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.54
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.55
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.44
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.21
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.85
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.98
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.59
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.08
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.08
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.42
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.73
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.73
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.69
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.46
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.53
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.45
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.41
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.12
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.96
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.90
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 181                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.12
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.06
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10255.21
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.42
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.13
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.26
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.51
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.61
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.29
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.75
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.82
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000155359
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.71
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000026431
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186875929.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27324
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 12                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.54
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.90
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.77
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.80
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.09
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.49
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.59
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.08
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.83
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.11
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.17
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.84
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.82
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.06
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908549
   j =  2                              :            45718
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46376
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870376
   j =  1                              :        399907252
   j =  2                              :            46368
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.23
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.98
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.01
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.45
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.80
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.92
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.14
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.77
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.31
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.19
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17454.66
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.09
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.69
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.69
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.31
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.31
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.18
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.04
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.05
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.63
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.70
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.53
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.46
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.07
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.01
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.55
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.24
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.16
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.33
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.21
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.50
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.11
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.35
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.38
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.99
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.02
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.92
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.88
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.01
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.57
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.05
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10250.48
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.07
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.02
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.28
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.84
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.72
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.39
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.35
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999919529
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.89
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000082651
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:27.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187826201.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27325
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7068
 p-value of test no 15                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.53
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.17
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.62
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.54
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.98
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.66
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.04
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.73
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.63
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.15
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.31
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.33
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.23
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.15
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908038
   j =  2                              :            45978
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908831
   j =  2                              :            45583
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.16
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.59
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.03
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.96
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.17
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.82
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.86
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.62
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.64
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.87
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17628.15
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.23
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.91
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.94
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.32
 p-value of test no 149                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.16
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.87
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.18
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.86
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.70
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.90
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.89
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.80
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.43
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.53
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.33
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.17
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.17
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.11
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.16
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.03
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.34
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.27
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.59
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.95
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.13
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.68
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.52
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.41
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.44
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.50
 p-value of test no 177                :    0.9937
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.59
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.23
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 200                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.75
 p-value of test no 203                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.76
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.47
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.64
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.02
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.54
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.31
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.16
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.04
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.91
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.39
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000102769
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.77
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999837446
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.089
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.54e-3
 p-value of test no 245                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.35
 p-value of test no 248                :  9.4e-3
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.07
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188776473.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27326
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.95
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 28                 :    0.9957
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.37
 p-value of test no 40                 :  6.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.94
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.91
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.42
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.90
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.02
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.41
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.69
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.32
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.86
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.76
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.09
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.34
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908619
   j =  2                              :            45689
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46211
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907585
   j =  2                              :            46197
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.42
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.67
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.03
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.34
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.53
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.15
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.70
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.26
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.65
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.77
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.38
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.14
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.19
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.05
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.37
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.38
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.87
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.03
 p-value of test no 156                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.17
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.65
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.89
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.00
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.55
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.23
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.64
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.96
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.74
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.03
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.93
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.77
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.66
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.31
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.90
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.16
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.34
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.49
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.98
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.16
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.63
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.01
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.09
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.70
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.81
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.90
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.72
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.60
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.42
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000018892
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.11
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999946256
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 247                :    0.9972
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:57.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189628441.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27327
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 33                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.98
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.47
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.89
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.27
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.86
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.59
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.34
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6718.49
 p-value of test no 57                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.41
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.99
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.30
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.40
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.90
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908198
   j =  2                              :            45895
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908709
   j =  2                              :            45641
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-3
 p-value of test no 76                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 78                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 115                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.72e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.90
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.08
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.63
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.28
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.82
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.79
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.79
 p-value of test no 133                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.78
 p-value of test no 135                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.66
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17595.86
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.46
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.42
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.82
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.35
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.59
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.62
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.56
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.78
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.00
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.39
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.52
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.26
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.10
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.97
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.51
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.89
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.25
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.78
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.46
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.19
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.03
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.60
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.85
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.08
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.24
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.89
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.15
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.97
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.85
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.22
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.89
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.59
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.15
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.72
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.76
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.15
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.64
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.76
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000019009
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.98
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000121837
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:59.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190644249.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27328
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7576
 p-value of test no 21                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.97
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.96
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.75
 p-value of test no 49                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.74
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.08
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.81
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.16
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.59
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.39
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.54
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.42
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.93
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.68
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.56
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908021
   j =  2                              :            45985
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908739
   j =  2                              :            45626
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.47
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.38
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.55
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.13
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.60
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.26
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.72
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.29
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17538.02
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.90
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.61
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.74
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.94
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.77
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.15
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.04
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.07
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.87
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.22
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.61
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.32
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.81
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.62
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.55
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.04
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.33
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.89
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.57
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.53
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.90
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  307.96
 p-value of test no 169                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.86
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.55
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.39
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.58
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.13
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.74
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.17
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.12
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.60
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.26
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.92
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.10
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10198.05
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 212                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.30
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.77
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.57
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.83
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.01
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.37
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12082.11
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.46
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999921674
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.52
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999969209
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:10.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191561753.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27329
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     825
 p-value of test no 25                 :    0.9940
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.24
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.53
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.21
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.93
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.88
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.41
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.06
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.97
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.78
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.28
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.58
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.09
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908064
   j =  2                              :            45962
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908851
   j =  2                              :            45570
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -8.03e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.53
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.95
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.60
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.05
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.98
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.62
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.08
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.07
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.79
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17754.73
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.09
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.15
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.23
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.98
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.84
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.65
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.40
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.71
 p-value of test no 153                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.40
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.02
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.71
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.38
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.86
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.08
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.63
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.22
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.01
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.62
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.63
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.14
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.71
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.32
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.66
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.35
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.89
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.55
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.27
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.78
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.36
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.37
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.01
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.30
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.12
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5118.43
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.32
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.75
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.72
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.89
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.13
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999909104
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.10
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999910118
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 241                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:12.77
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192512025.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27330
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5580
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4158
 p-value of test no 17                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.65
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.07
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.72
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.89
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.33
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.83
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.33
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.43
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.37
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.49
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.36
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.63
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.26
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.61
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5201.16
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907860
   j =  2                              :            46064
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46203
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907599
   j =  2                              :            46193
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9905
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.68
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.92
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.73
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.72
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.27
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.52
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.76
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.80
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17578.90
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.17
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.95
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.14
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.03
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.82
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.70
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.28
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.22
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.84
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.52
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.07
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.76
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.93
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.64
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.54
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.67
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.00
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.59
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.09
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.38
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.81
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.37
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.75
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.41
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.16
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.67
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.09
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.72
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.84
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    2.38
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.05
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.30
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.71
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.10
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.13
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 213                :  9.9e-4    *****
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 214                :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10433.09
 p-value of test no 215                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.13
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.75
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.92
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.35
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.05
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.20
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.17
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999909572
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.64
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000047605
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:56.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193527833.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27331
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 17                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 30                 :    0.9962
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.14
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.23
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.99
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.07
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.95
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.45
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.13
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.18
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.13
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.79
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.93
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.15
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.44
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.61
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908337
   j =  2                              :            45827
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908132
   j =  2                              :            45931
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.42
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.02
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.98
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.90
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.53
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.68
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.51
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.72
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.41
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 139                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 140                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  176.70
 p-value of test no 141                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.43
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.52
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.64
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.48
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.36
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.83
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.81
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.55
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.02
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.99
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.71
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.48
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.40
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.24
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.49
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.22
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.47
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.10
 p-value of test no 165                :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.93
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.60
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.28
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.20
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.39
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.70
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.37
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.35
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.98
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.00
 p-value of test no 175                :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.46
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.35
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.72
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.17
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.62
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.39
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.47
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.29
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.99
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.45
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.88
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.56
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.48
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999893258
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.69
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999875552
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9957
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:46.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194740249.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27332
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.26
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.25
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.85
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.41
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.96
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.37
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.07
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.01
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.67
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9908
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.36
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.29
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.43
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.64
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.86
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907971
   j =  2                              :            46013
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908151
   j =  2                              :            45920
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.25
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.27
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.17
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.89
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.83
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.83
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.47
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 131                :  4.9e-4    *****
 
 Anderson-Darling statistic = A2       :    7.61
 p-value of test no 132                :  1.9e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   76.40
 p-value of test no 133                :  4.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.88
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 143                :    0.9926
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17095.27
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.84
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.78
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.50
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.50
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.01
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.10
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.29
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.67
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.94
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.45
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.76
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.43
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.63
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.07
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.46
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.99
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.88
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.55
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.70
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.05
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.50
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.31
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.80
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.92
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.76
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.88
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.93
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 200                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 201                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.99
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.05
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 208                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10298.09
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.03
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5091.45
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.72
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.54
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.53
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11551.85
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.75
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.01
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000016042
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.53
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000063961
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:50.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          4.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195756057.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27333
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.38
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.64
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.45
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.74
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.99
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.31
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.21
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.84
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.99
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.42
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.99
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.47
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.82
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5171.67
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908532
   j =  2                              :            45731
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.17
 p-value of test no 119                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.86
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.57
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.62
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.63
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.30
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.22
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.03
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.78
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.25
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.65
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.55
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.73
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.63
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.38
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.50
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.80
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.36
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.01
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.69
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.08
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.13
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.44
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.87
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.51
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.50
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.97
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.06
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.25
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.14
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.31
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.79
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.39
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.57
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.68
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.34
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.81
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.35
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.41
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.40
 p-value of test no 217                :  3.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.76
 p-value of test no 218                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.62
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.12
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.26
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.51
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.67
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.40
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.12
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999827447
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.68
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999796040
 
 Normal statistic for number of bits   :   -1.61
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.64
 p-value of test no 248                :  4.2e-3
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:02.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300            3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196739097.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27334
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.92
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.92
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.04
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.97
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.32
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.62
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1572.03
 p-value of test no 56                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.33
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.35
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.89
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.89
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.36
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908194
   j =  2                              :            45897
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907661
   j =  2                              :            46168
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 83                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.99
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.71
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.84
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.78
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.09
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.66
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.33
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.25
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.60
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.92
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.16
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.82
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.25
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.56
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.25
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.82
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.31
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.37
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.45
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.05
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.30
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.52
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.76
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.72
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.29
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.89
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.71
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.53
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.16
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.85
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.79
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.24
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.72
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.23
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.31
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.48
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.33
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.99
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.14
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.68
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.94
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.76
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.13
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5126.36
 p-value of test no 222                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.60
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.17
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.96
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.46
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.55
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.69
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999940136
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.40
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000102211
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:17.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197754905.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27335
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997123
   j =  2                              :             1437
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.69
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.81
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.46
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.75
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.58
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.86
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  287.26
 p-value of test no 54                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.85
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.95
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.10
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.22
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.51
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.67
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.24
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908349
   j =  2                              :            45818
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907791
   j =  2                              :            46100
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.36
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.26
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.94
 p-value of test no 123                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.39
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 126                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.90
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.49
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.03
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17637.29
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.11
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.28
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.15
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.25
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   14.48
 p-value of test no 151                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.23
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.73
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.60
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.16
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.63
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.62
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.79
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.56
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.38
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.74
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.33
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.06
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.41
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.63
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.67
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.32
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.21
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  485.11
 p-value of test no 172                :  3.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5194.20
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.26
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.60
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.67
 p-value of test no 176                :  6.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.16
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.30
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.38
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.35
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.41
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9680.95
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.95
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.35
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.68
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.26
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.50
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.92
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.46
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000040582
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.41
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000018406
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:31.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      0.9995 
  79  RandomWalk1 M (L=10000, r=15)   3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198705177.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27336
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.59
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.62
 p-value of test no 29                 :  1.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    3.22
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.23
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.73
 p-value of test no 47                 :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.23
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.26
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.64
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.92
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.32
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.68
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.07
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.42
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.98
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.54
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.22
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.27
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5196.05
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908021
   j =  2                              :            45985
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907779
   j =  2                              :            46097
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 72                 :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  8.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.39
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.35
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.80
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.26
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.66
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.19
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.11
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.48
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.65
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.76
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.31
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.87
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.66
 p-value of test no 149                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.94
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.21
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.61
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.27
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.73
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.79
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.15
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.10
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.88
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.69
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.91
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.24
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.83
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.67
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.36
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.98
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.33
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.67
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.55
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.24
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.02
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.07
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.22
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.75
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.09
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.05
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.26
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 188                :    0.08
 
 Sample variance                       :    2.40
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.56
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.81
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.48
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.84
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.37
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.16
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.27
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.84
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.54
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.78
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999974126
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.60
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999975053
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:42.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199622681.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27337
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 12                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    2.75
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.63
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.50
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.05
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.57
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.77
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.33
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.94
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.36
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.38
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.41
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.42
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.08
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.27
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.65
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.09
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45573
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908857
   j =  2                              :            45567
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907989
   j =  2                              :            45998
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 111                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.63
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  110.62
 p-value of test no 120                :  6.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.36
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.49
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.45
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.43
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.44
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.20
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.80
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.50
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17716.06
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.04
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.87
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.86
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.05
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.24
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.15
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.12
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.86
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.52
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.45
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.28
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.97
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.82
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.70
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.57
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.65
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.76
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.83
 p-value of test no 165                :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.02
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.24
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.23
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.75
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.85
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.99
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.87
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.16
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.59
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.05
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.30
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.47
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.40
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.92
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.39
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.22
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.02
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.05
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.75
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.70
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.08
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.76
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000145882
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.77
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000051205
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 240                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200638489.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27338
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 11                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4550
 p-value of test no 17                 :  6.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    4.87
 p-value of test no 30                 :  3.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     539
 p-value of test no 31                 :    0.9939
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    5.10
 p-value of test no 33                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.17
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.22
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.79
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.39
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.66
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.07
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.27
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7154.85
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.90
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.32
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.51
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.81
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.24
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908051
   j =  2                              :            45970
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908625
   j =  2                              :            45680
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.43
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.98
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.98
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.08
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.76
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.66
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.22
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.03
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.59
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.40
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17379.45
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.31
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.75
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.57
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.67
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.65
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.09
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.89
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.84
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.05
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.38
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.46
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.06
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.30
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.39
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.93
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.29
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.17
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.53
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.93
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.94
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.68
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.96
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.71
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.47
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.71
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.80
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.74
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.29
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 181                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 182                :  4.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.96
 p-value of test no 183                :  1.6e-3
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.90
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.80
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.63
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.47
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.05
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.09
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.01
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.97
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.33
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.77
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.70
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.01
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.44
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000070987
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.81
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000086611
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.19
 p-value of test no 249                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:52.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         6.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201621529.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27339
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.97
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.37
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.69
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.90
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.14
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.94
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.89
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7281.96
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.00
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.99
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.34
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.54
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5267.43
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907842
   j =  2                              :            46073
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908495
   j =  2                              :            45748
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
 p-value of test no 98                 :    0.9960
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.59
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.02
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.14
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.80
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.47
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.01
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.76
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.49
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.93
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.15
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.83
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.86
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.20
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.20
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.21
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.40
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.64
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.40
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.06
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.05
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.95
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.21
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.08
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.19
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.71
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.85
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.51
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.96
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.21
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.12
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.84
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.14
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.74
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.10
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.75
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.44
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.99
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.50
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.90
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.43
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.26
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.99
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.40
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.86
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.88
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.44
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.38
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.43
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.25
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.55
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.46
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.61
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.53
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000087373
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.49
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000045838
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
 p-value of test no 240                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    5.70
 p-value of test no 242                :  1.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.28
 p-value of test no 243                :  5.2e-4    *****
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:01.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  104  AutoCor, d=3, r=0               5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202604569.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27340
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.74
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9922
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    2.94
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.11
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.03
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.94
 p-value of test no 49                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.72
 p-value of test no 50                 :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.94
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.41
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.09
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.17
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.88
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.23
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.60
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.99
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.64
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.98
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907827
   j =  2                              :            46076
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908684
   j =  2                              :            45655
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 107                :  1.0e-3
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 108                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.03
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.45
 p-value of test no 120                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.64
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.83
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.77
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.24
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.22
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.08
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.31
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 143                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17812.74
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.05
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.45
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.20
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.79
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.37
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.90
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.65
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.15
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.58
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.26
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.84
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.50
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.51
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.24
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.72
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.09
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.47
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.75
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.25
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.04
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.42
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.91
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.33
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.41
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.90
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.58
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.04
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.44
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.50
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.02
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.45
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.82
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.00
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.91
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.80
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.40
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 220                :    0.9924
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4690.88
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 224                :    0.9914
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4694.64
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.99
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.96
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.19
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.03
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.43
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999882974
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.46
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000013858
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:34.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183828506.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27341
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.55
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.47
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.20
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.66
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.76
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.13
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.62
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.91
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.49
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.72
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.09
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.95
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.30
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.35
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5182.69
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908303
   j =  2                              :            45841
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907922
   j =  2                              :            46036
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-5
 p-value of test no 113                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.56
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.93
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.30
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.40
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.64
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.40
 p-value of test no 124                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.85
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.73
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.06
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.18
 p-value of test no 137                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.00
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.39
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.40
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.11
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.43
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.35
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.07
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.84
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.78
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.46
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.37
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.68
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.72
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.45
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.98
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.14
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.80
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.16
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.95
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.57
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.28
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.44
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.31
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.96
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.03
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.77
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.58
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.77
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.79
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.66
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.41
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.59
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.86
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.97
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.10
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.93
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.64
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.22
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.39
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.99
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.28
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.74
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.84
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000140101
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.14
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000060067
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:43.48
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184713242.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27342
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.46
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.42
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.51
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.76
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.99
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.84
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.83
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.64
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.58
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.94
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.28
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.35
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.55
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.11
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908067
   j =  2                              :            45965
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908275
   j =  2                              :            45861
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9943
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-4
 p-value of test no 83                 :    0.9990    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 92                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.10
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.59
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.93
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.11
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.36
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.21
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.03
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.55
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17461.69
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.97
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.57
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.18
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.40
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.90
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.56
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.57
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.60
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.34
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.95
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.31
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.90
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.79
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.48
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.63
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.73
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.12
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.08
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.29
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.86
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.43
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.57
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.84
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.49
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4750.13
 p-value of test no 173                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.46
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.25
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.34
 p-value of test no 176                :  6.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.01
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.90
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.90
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.26
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.60
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.39
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.92
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.03
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5070.14
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4683.36
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.31
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.31
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.63
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.98
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.45
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999893840
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.99
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000099091
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    2.12
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:00.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185565210.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27343
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 33                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.60
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.39
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.50
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.36
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.85
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.90
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.98
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.91
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.58
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.56
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.77
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.92
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.97
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908355
   j =  2                              :            45815
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908687
   j =  2                              :            45649
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.71
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.71
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.30
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.88
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.13
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.13
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.04
 p-value of test no 125                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.02
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.41
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.35
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.86
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.93
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.13
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.70
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.44
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.52
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.05
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.70
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.98
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.81
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.98
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.80
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.49
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.61
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.06
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.16
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.51
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.46
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.22
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.41
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.72
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.76
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.91
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.86
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.62
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.57
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.52
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.89
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.77
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.54
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.57
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.58
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.77
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4731.09
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.03
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.31
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.36
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11490.77
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.08
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.69
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000043273
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.45
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999864557
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:09.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186581018.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27344
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 8                  :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.23
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.56
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.95
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.72
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.37
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.46
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.52
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.50
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6820.16
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.26
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.44
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.59
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.00
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.90
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908510
   j =  2                              :            45736
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46327
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870327
   j =  1                              :        399907351
   j =  2                              :            46317
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 90                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.16
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.28
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.86
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.34
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.93
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.25
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.53
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.36
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17787.37
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.65
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.12
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.05
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.44
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.02
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.73
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.67
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.68
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.06
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.70
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.02
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.33
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.62
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.17
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.84
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.86
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.35
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.93
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.55
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.07
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.59
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.22
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.48
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.01
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.84
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.45
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.28
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.55
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.38
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.90
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10266.81
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 216                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.70
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4732.87
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.21
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.97
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.70
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.48
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.52
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999952970
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.62
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000022597
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:40.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187924506.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27345
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 15                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    3.58
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 34                 :    0.9981
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.82
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.81
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.22
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.15
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.47
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.68
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.13
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.48
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.06
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.39
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.54
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.78
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908047
   j =  2                              :            45969
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908008
   j =  2                              :            45993
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.86
 p-value of test no 118                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.43
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.20
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.53
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.22
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.61
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.36
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.84
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17282.20
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.11
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.74
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.24
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.18
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.43
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.63
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.35
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.43
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.51
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.68
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.05
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.30
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.27
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.02
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.57
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.87
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.18
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.97
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.29
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.09
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.48
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.10
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.65
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.51
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.17
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.91
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.99
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.27
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.61
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.26
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.08
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.09
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.63
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.05
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.60
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.08
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.00
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000147019
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000072880
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:42.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188842010.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27346
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 4                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.62
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    6.98
 p-value of test no 44                 :  3.5e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.63
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.59
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.01
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.64
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.52
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.64
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.23
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.09
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.11
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.66
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.66
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.90
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.79
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.51
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45604
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908797
   j =  2                              :            45594
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908353
   j =  2                              :            45819
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.57
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.63
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.93
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.28
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.87
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.87
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.31
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.59
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.98
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.81
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17615.40
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.09
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.13
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.93
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.02
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.84
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.34
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.62
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.10
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.08
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.37
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.07
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.04
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.02
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.06
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.69
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.54
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.91
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.87
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.36
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.26
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.86
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.70
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.37
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.25
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.50
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.83
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.42
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.13
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.05
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.42
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.61
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.45
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.05
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.30
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.24
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.09
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.37
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.43
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.52
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.75
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.62
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.57
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.22
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999921638
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.01
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999930902
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:33.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189890586.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27347
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.86
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.20
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.24
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.23
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.19
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.98
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.50
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.95
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.31
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.49
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.86
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.59
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.43
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.33
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908509
   j =  2                              :            45744
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907739
   j =  2                              :            46120
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
 p-value of test no 80                 :    0.9962
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 8.11e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.42
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.85
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.51
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.63
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.94
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.07
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.06
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.17
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.59
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.31
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.57
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.38
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.26
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.65
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.53
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.41
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.79
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.95
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.98
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.17
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.19
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.19
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.20
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.64
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.87
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.29
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   98.45
 p-value of test no 164                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.90
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.24
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.52
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.30
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.35
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.06
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.05
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.86
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.69
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.86
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.79
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.91
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.03
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.09
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.50
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.05
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.51
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.12
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.19
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.66
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.15
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.54
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.23
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.39
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.96
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.25
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000061495
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.48
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000027748
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:03.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191070234.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27348
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    3.71
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.25
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.92
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.98
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.24
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.68
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.97
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.66
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.55
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.91
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.77
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.56
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.10
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.71
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908219
   j =  2                              :            45883
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45615
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908773
   j =  2                              :            45609
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.97
 p-value of test no 119                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.15
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.37
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.78
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.71
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.69
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.56
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.67
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.73
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.04
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.09
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.86
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.20
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.38
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.97
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.30
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.62
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.29
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.53
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.51
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.06
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.44
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.27
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.10
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.69
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.62
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.68
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.66
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.54
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.31
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.38
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.19
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.86
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.80
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.09
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.99
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.71
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.10
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 195                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.80
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.12
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.93
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.68
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.35
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.19
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.75
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.73
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3897.62
 p-value of test no 227                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.74
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.93
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.51
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.84
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000028219
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.52
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000126568
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9909
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:39.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192086042.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27349
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    3.72
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     118
 p-value of test no 43                 :    0.9961
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.77
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.44
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.58
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.50
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.93
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.73
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.43
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.80
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.88
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.88
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.19
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.30
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.16
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908579
   j =  2                              :            45706
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907588
   j =  2                              :            46200
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.55
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.51
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.03
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.23
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.75
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 128                :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.36
 p-value of test no 129                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.23
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.63
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.90
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17733.79
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.63
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.00
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.10
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.97
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.21
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.48
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.13
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.08
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.40
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.94
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.78
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.67
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.50
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.94
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.33
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.02
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.99
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.94
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.13
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.14
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.32
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.23
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.55
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.71
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.22
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.53
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.00
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.27
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.38
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.68
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.84
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.99
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.77
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.28
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.49
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 223                :  6.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    6.29
 p-value of test no 225                :  7.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4579.20
 p-value of test no 226                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.41
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.25
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.01
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.37
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.92
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999908690
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.88
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000020458
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.41
 p-value of test no 248                :    0.9920
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:54.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  96  HammingIndep, L=30, r=27        0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193036314.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27350
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    5.70
 p-value of test no 39                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.15
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.45
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.71
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.12
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.34
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.60
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.11
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.23
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7166.04
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 60                 :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.87
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.21
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.47
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.72
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907862
   j =  2                              :            46063
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908146
   j =  2                              :            45924
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.92
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.65
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.00
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.64
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.18
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.25
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.62
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.55
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.62
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.74
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.80
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.89
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.45
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.36
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.11
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.81
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.61
 p-value of test no 154                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.85
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.52
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.98
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.63
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.84
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.45
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.60
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.31
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.19
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.38
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.96
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.48
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.04
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.10
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.50
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.91
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.27
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5190.86
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.68
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.87
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.37
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.71
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.36
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.36
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.11
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 212                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.76
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.65
 p-value of test no 217                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.31
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.15
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4269.95
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.95
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.09
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.38
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.62
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999970421
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.46
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000070516
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:08.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194052122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27351
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    3.43
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     249
 p-value of test no 37                 :    0.9986
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.98
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.54
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.22
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.21
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.84
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.99
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.19
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.60
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.69
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.20
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.58
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.95
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45698
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869698
   j =  1                              :        399908607
   j =  2                              :            45692
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908412
   j =  2                              :            45785
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.47
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.95
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.73
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.80
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.64
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.72
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.86
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.15
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.67
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.72
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.06
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.52
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.91
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.61
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.89
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.40
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.02
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.43
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.22
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.30
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.77
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.43
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.66
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.21
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.12
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.64
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.33
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.37
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.14
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.05
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.50
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.58
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.32
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.26
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.91
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.41
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.13
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.50
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.90
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.46
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.20
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.39
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.99
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.79
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.88
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.62
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.10
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 218                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.11
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.25
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.33
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.86
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.89
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.64
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.35
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000018118
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.99
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999990563
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:55.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195067930.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27352
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.18
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.39
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.09
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.14
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.32
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.49
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.27
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.18
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.21
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.90
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.20
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.95
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.80
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.11
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.30
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908697
   j =  2                              :            45650
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908089
   j =  2                              :            45942
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 79                 :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  8.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.46
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.67
 p-value of test no 120                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.01
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.36
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.29
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.07
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.82
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.46
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17158.36
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.04
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.56
 p-value of test no 147                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.49
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.55
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.14
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.06
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.01
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.60
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.42
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.60
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.80
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.76
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.48
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.08
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.81
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  197.62
 p-value of test no 164                :  4.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.84
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.09
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.89
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.80
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.35
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.52
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.12
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.41
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.78
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.74
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.80
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.04
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.33
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.38
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.69
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.84
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.16
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.59
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.53
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.96
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.71
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.53
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.34
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999969938
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.24
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999997295
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.91
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:30.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196083738.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27353
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.43
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.42
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.81
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.13
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.28
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.25
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.66
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.17
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.90
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.41
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.26
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.82
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.11
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908418
   j =  2                              :            45782
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907764
   j =  2                              :            46115
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.99
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.19
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.28
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.79
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.52
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.41
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.31
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.45
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.04
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17615.32
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.68
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.52
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.78
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.80
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.97
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.47
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.69
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.09
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.90
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.90
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.95
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.57
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.25
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.87
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.93
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.58
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.48
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.51
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.24
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.61
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.80
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.92
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.64
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.89
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.18
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.17
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.97
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.57
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.27
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.12
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.99
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.00
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 213                :    0.9923
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9777.46
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.07
 p-value of test no 217                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.84
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.73
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.66
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.06
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.53
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.64
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.54
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999926546
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.73
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000021910
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.083
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:55.42
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197066778.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27354
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 12                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9925
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.69
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.34
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.05
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.87
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.60
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.39
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.49
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  368.85
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.76
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.78
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.17
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.65
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.77
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.67
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908434
   j =  2                              :            45777
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908197
   j =  2                              :            45900
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.21
 p-value of test no 118                :  6.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.47
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.73
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.09
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.62
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.77
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.23
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.00
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-3
 p-value of test no 138                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.91
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17144.68
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.34
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.18
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.38
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.00
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.68
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.04
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.27
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.81
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.58
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.36
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.67
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.68
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.70
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.74
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.16
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.46
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.79
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.58
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.23
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.93
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  482.38
 p-value of test no 167                :  4.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.86
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.55
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.67
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.86
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.68
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.39
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.46
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.47
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.15
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.93
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 183                :    0.03
 
 Sample variance                       :    2.78
 p-value of test no 184                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.00
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.22
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9936
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.31
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.68
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.89
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.71
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.28
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.14
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.92
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.87
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.29
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.76
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000053911
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.50
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000003388
 
 Normal statistic for number of bits   :   0.027
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.045
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:34.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  58  AppearanceSpacings, r = 27      6.5e-4
  78  RandomWalk1 M (L=10000, r=0)    4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198049818.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27355
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9915
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     540
 p-value of test no 31                 :    0.9931
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.91
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.13
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.91
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.49
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.52
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.63
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.09
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.73
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.45
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.15
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.30
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.31
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.20
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908308
   j =  2                              :            45846
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45620
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869620
   j =  1                              :        399908770
   j =  2                              :            45600
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.01
 p-value of test no 119                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.06
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.51
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.57
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.84
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.15
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.34
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.86
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.49
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17626.50
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.56
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.55
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.19
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.29
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.60
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.13
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.87
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.98
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.81
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.84
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.34
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.61
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.61
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.89
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.39
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.35
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.66
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.99
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.68
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.90
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.14
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.92
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.35
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.29
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.01
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.03
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.78
 p-value of test no 175                :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.30
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.44
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.83
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.72
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.25
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.18
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.55
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.00
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.77
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.98
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.61
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.28
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.46
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000000172
 
 Normal statistic for number of bits   : 1.36e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.67
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999921011
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 246                :    0.9963
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 247                :  6.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.76
 p-value of test no 248                :    0.9971
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:35.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199000090.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27356
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.62
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    3.00
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.75
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.26
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.49
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.12
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.79
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.64
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.00
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.21
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.58
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.31
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.96
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.74
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.53
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908579
   j =  2                              :            45706
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908192
   j =  2                              :            45901
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 98                 :  9.5e-4    *****
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 99                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.46
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.51
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.33
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.63
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.92
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.29
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.19
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 138                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  174.67
 p-value of test no 141                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.50
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.10
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.76
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.80
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.59
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.00
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.00
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.03
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.98
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.67
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.21
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.77
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.10
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.25
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.77
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.26
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.94
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.00
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.59
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.00
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.91
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.55
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.58
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.68
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.50
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.20
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.32
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.13
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.02
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.97
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.35
 p-value of test no 183                :    0.9906
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.94
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.34
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.29
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.01
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.82
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.52
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.51
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.29
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.26
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.77
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.31
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.02
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.28
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999994739
 
 Normal statistic for number of bits   :  -0.042
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.10
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999783230
 
 Normal statistic for number of bits   :   -1.71
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200015898.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27357
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    3.72
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.61
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.31
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.79
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.30
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.47
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1275.39
 p-value of test no 56                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.80
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.16
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.88
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.22
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.61
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.32
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908340
   j =  2                              :            45827
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908097
   j =  2                              :            45947
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 92                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.52
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.45
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.46
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.36
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.20
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.27
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.52
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.60
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.89
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.58
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.80
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.90
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.71
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.90
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.91
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.28
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.84
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.67
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.90
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.60
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.69
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.73
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.32
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.13
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.14
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.29
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.50
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.82
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.00
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.19
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.84
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.64
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.78
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.37
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.60
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.79
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.58
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.89
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.25
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.13
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.39
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    2.17
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.15
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.34
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.59
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.46
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.59
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.09
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.32
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.67
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.99
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.18
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.80
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.84
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000018961
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.06
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999951560
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:10.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200933402.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27358
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 5                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 11                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7588
 p-value of test no 18                 :  8.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.74
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   43.66
 p-value of test no 49                 :  6.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.47
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.03
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.98
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.46
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.06
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.60
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.84
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.01
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.02
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.72
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.77
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46107
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907789
   j =  2                              :            46101
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907807
   j =  2                              :            46095
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 84                 :  6.3e-5    *****
 
 Anderson-Darling statistic = A2       :    7.39
 p-value of test no 85                 :  2.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 98                 :    0.9900
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-6
 p-value of test no 109                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 111                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.03
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.77
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.82
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.10
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.26
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.81
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.45
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.33
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17217.94
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.31
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.95
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.63
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.75
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.77
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.61
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.76
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.15
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.72
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.65
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.59
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.73
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.63
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.15
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.83
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.45
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.27
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.90
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.78
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.25
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.54
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.31
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.01
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.17
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.60
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.00
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.23
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.69
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.35
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.67
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.47
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.50
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.64
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.00
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.70
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.05
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12090.30
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.47
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.39
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999919817
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.13
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000056581
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:33.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         8.8e-4
  29  SimpPoker, r = 25               6.4e-4
  47  MaxOft AD, t = 16               2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201883674.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27359
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     661
 p-value of test no 31                 :  7.4e-3
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    6.19
 p-value of test no 36                 :  8.1e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     260
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9926
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.73
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.88
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.99
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.32
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.74
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.71
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.11
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.09
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.38
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.31
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7380.71
 p-value of test no 57                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.96
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.45
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.77
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.64
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.17
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908717
   j =  2                              :            45637
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907783
   j =  2                              :            46107
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.43
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.55
 p-value of test no 120                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.59
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.19
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.13
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.30
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.96
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.11
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.68
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.62
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.18
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.08
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.55
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.52
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.79
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.73
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.61
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.02
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.16
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.68
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.26
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.65
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.41
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.35
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.54
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.27
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.14
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.94
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.22
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.56
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.34
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.55
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.24
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.80
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.40
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.35
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.89
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.40
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.17
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.87
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.23
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.68
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.12
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.46
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
 p-value of test no 219                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5150.62
 p-value of test no 222                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.38
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4368.22
 p-value of test no 227                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.53
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.08
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.31
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.56
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000000997
 
 Normal statistic for number of bits   : 7.88e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.35
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999941213
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 246                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 247                :  9.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.35
 p-value of test no 248                :  9.4e-3
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:57:28.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          8.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202997786.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27360
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 9                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9905
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.95
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.79
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.23
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.03
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.57
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.70
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.55
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.18
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.25
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.26
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.71
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.91
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.45
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.26
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4840.56
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907691
   j =  2                              :            46150
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45394
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869394
   j =  1                              :        399909215
   j =  2                              :            45388
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-4
 p-value of test no 104                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.23
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.91
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.17
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.96
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.67
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.33
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.61
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.98
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.74
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.91
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.52
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.94
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.07
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.76
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.47
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.76
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.81
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.20
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.88
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.82
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.43
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.07
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.90
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.85
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.44
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.34
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.58
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.70
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.06
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.19
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.93
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.98
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.29
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.88
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.16
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.65
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.65
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.52
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.55
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.42
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.11
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.30
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.25
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.34
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.89
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.85
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.25
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.63
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.03
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.89
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.80
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.72
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000075376
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.93
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000103156
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:15:34.11
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183861275.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27361
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 35                 :    0.9982
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.34
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.29
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.35
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.46
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.07
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.54
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.67
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.78
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.37
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.99
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.11
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.97
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.13
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.15
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.09
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.60
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45456
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869456
   j =  1                              :        399909091
   j =  2                              :            45450
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907944
   j =  2                              :            46028
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.08
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.55
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.64
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.91
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.71
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.87
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.97
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.55
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.88
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.17
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.57
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17540.41
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.37
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.89
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.68
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.93
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.85
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.20
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.64
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.64
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.61
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.21
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.23
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.32
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.22
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.75
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.35
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.32
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.04
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.46
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.15
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.03
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.58
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.76
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.58
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.03
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.02
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.74
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.56
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.74
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.70
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.73
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.96
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.13
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.21
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.82
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.46
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.85
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.61
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.59
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.64
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12250.90
 p-value of test no 230                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.78
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999973079
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.47
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000085927
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:01.43
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184811547.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27362
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.53
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.89
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.16
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.66
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.09
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.42
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.86
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.36
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.96
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.10
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.28
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.55
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.75
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.76
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.65
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4831.02
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46583
 p-value of test no 70                 :  5.3e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870583
   j =  1                              :        399906837
   j =  2                              :            46577
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907797
   j =  2                              :            46094
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 72                 :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 74                 :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  2.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.08
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.63
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.37
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.69
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.26
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.14
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.57
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.95
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.93
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.46
 p-value of test no 134                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.45
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17555.95
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.09
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.11
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.26
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.37
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.86
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.94
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.35
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.74
 p-value of test no 155                :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.96
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.31
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.78
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.46
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.25
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.65
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.66
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.13
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.08
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.86
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.83
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.59
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.09
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.78
 p-value of test no 170                :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.13
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.76
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.96
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.71
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.11
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.46
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.29
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.50
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.61
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.84
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5046.48
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.16
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4268.07
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.47
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.00
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11537.60
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.51
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999886679
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.74
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000142705
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:25.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  44  CollisionPermut, r = 0          5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185925659.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27363
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7521
 p-value of test no 20                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.39
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.75
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.69
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.81
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.06
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.63
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.11
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.81
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.17
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.23
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.56
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.65
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.78
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.61
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908464
   j =  2                              :            45762
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908046
   j =  2                              :            45974
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.12
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.85
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.29
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.77
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.37
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.83
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.27
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.64
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.02
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.56
 p-value of test no 137                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.41
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17067.14
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.68
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.73
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.51
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.67
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.45
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.30
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.25
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.81
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.42
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.06
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.26
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.49
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.84
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.36
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.01
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.34
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.62
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.23
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.18
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.12
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.48
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.99
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.71
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.36
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.83
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.68
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.18
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.36
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.42
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.27
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.55
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.87
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.28
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.77
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.36
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.96
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.13
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.43
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.26
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.59
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.75
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.02
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.45
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.09
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000086701
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.02
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000121054
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:36.46
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186744859.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27364
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1485
 p-value of test no 9                  :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5600
 p-value of test no 13                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.38
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.43
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.39
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.10
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.18
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.60
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.53
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.35
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.59
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.09
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.00
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.76
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.78
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908532
   j =  2                              :            45728
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907963
   j =  2                              :            46014
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 79                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 81                 :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 86                 :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 88                 :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9949
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 97                 :  5.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    5.18
 p-value of test no 99                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.96
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.33
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.40
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.11
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.36
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.87
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.09
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.26
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.27
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.77
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17525.40
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.95
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.48
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.33
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.08
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.15
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.30
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.95
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.23
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.85
 p-value of test no 156                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.01
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.53
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.24
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.88
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.18
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.24
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.68
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.60
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.80
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.00
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.80
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.06
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.68
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.98
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.70
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.64
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.68
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.09
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.65
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.78
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.52
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.10
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.44
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.09
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9758.30
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.44
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.84
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.09
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.50
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.24
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.89
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.70
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999914267
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.73
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999860135
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 235                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:36.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187629595.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27365
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9980
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 3                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.09
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.76
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.18
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.62
 p-value of test no 52                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.19
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.49
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.70
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1597.89
 p-value of test no 56                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.13
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.48
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.64
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.81
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.96
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908617
   j =  2                              :            45687
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908262
   j =  2                              :            45860
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
 p-value of test no 106                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.94
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.09
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.48
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.28
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.23
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.38
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.49
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.96
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.51
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.23
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.73
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.04
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.39
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.24
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.85
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.24
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.70
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.31
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.50
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.95
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.43
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.27
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.61
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.08
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.39
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.94
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.00
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.78
 p-value of test no 165                :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.99
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.84
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.97
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.34
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.10
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.40
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.99
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.99
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.35
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.87
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.37
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.09
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.88
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.49
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.86
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.65
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.27
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.76
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12029.48
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.83
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.75
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000082639
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.05
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000017008
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    2.62
 p-value of test no 239                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:57.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188612635.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27366
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    3.16
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    3.89
 p-value of test no 45                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.61
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.63
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.84
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.69
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.21
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.73
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.87
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7275.46
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.29
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.26
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.34
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.02
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.16
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908521
   j =  2                              :            45732
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908475
   j =  2                              :            45761
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 90                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.51
 p-value of test no 115                :  2.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.58
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.32
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.88
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.98
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.39
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.18
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.77
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.73
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.20
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.83
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.41
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.43
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.56
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.81
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.56
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.29
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.32
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.08
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.76
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.77
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.59
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.87
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.80
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.49
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.96
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.49
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.96
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.74
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.80
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.10
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.17
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.79
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.43
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.25
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.60
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.27
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.82
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.47
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.30
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.33
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.68
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.15
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.29
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.84
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.43
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.51
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.26
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.59
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12103.30
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.81
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999852038
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.90
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999979190
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  55  SampleCorr, k = 1               2.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189530139.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27367
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     657
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.18
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.60
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.39
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.46
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.96
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.16
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1560.08
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.38
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.41
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.09
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.38
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.05
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908152
   j =  2                              :            45918
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908314
   j =  2                              :            45840
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.89
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.20
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.73
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.86
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.20
 p-value of test no 125                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.59
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.67
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.42
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17280.81
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.09
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.19
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.60
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.46
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.01
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.97
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.12
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.67
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.83
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.36
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.82
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.72
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.04
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.20
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.63
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.62
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.79
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.64
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.30
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.11
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.25
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.40
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  142.94
 p-value of test no 170                :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.85
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.60
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.89
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.70
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.11
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.34
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.15
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.99
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.46
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.72
 p-value of test no 198                :    0.9995    *****
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.83
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.39
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.08
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10308.28
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.30
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.41
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.55
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.89
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.80
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.76
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.37
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999945020
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.93
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000069259
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:23.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 C (L=10000, r=0)    0.9992 
  87  LongestHeadRun, r = 27          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190480411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27368
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4179
 p-value of test no 14                 :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.01
 p-value of test no 41                 :  9.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.02
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.01
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.17
 p-value of test no 49                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.37
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.23
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.18
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.75
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.87
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.13
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.73
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.76
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.94
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.89
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.54
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.56
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908639
   j =  2                              :            45676
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908735
   j =  2                              :            45628
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 118                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.15
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.79
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.03
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.66
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.53
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.72
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.00
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 126                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.73
 p-value of test no 129                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.43
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.13
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.83
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.82
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.17
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.30
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.83
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.95
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.12
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.40
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.08
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.86
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.21
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.00
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.76
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.36
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.40
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.93
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.80
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.62
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.62
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.22
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.54
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.27
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.31
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.21
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.08
 p-value of test no 171                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.90
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.80
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.28
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.77
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.97
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.90
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.28
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.99
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.42
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.50
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.56
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.12
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.36
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.21
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.47
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.16
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999988721
 
 Normal statistic for number of bits   :  -0.089
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.01
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999983978
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:00.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191430683.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27369
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.34
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.93
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.26
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.36
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.11
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.47
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.15
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.68
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.86
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.45
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.85
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.60
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.05
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.40
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908675
   j =  2                              :            45658
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908701
   j =  2                              :            45645
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.9e-3
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 101                :    0.9947
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 102                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-5
 p-value of test no 113                :    0.9916
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 114                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.42
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.75
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.85
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.20
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.36
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.05
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.97
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.65
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.16
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.19
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.40
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.35
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.59
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.67
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.46
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.48
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.11
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.78
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.10
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.56
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.46
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.08
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.74
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.84
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.87
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.88
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.66
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.37
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.91
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.42
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.84
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.88
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.30
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.98
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.81
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.29
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.03
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.66
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.24
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.77
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10258.73
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.55
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.97
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.02
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.98
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.64
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.89
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.98
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.43
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999937064
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.58
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999954113
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:33.42
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192413723.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27370
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 9                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    3.58
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    3.83
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.64
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.61
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.32
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.40
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.75
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.69
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.58
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.69
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.44
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.86
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.39
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907985
   j =  2                              :            46003
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907974
   j =  2                              :            46007
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.58
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.02
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.62
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.35
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.37
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.47
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.98
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.05
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.86
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.20
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17646.21
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.30
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.49
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.70
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.62
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.97
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.07
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.69
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.45
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.28
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.16
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.15
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.93
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.06
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.67
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.96
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.74
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  591.45
 p-value of test no 163                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.47
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.06
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.92
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.57
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.63
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.59
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.41
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.16
 p-value of test no 171                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.52
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.31
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.76
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.97
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.71
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.59
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    2.06
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.22
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.25
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.91
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.80
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.13
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.77
 p-value of test no 217                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.89
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.08
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.77
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.82
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.80
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.92
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.50
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000188293
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.32
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999948686
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:35.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193429531.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27371
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5559
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.08
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.89
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.64
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.10
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.54
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.60
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.48
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.64
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.66
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.93
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6815.53
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.47
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.14
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.65
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.27
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.98
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908384
   j =  2                              :            45802
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908544
   j =  2                              :            45725
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.29
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.15
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.22
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.32
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.04
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.71
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.17
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.49
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.42
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.47
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.46
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.52
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.63
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.56
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.17
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.76
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.08
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.40
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.58
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.42
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.21
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.57
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.08
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.99
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.83
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.09
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.82
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.56
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.17
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.84
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.55
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.10
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.06
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.97
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.58
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.46
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.53
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.50
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.45
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.58
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.33
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.96
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 208                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 210                :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9639.61
 p-value of test no 211                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.67
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.10
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.84
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4374.59
 p-value of test no 227                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.81
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12068.58
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.83
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.53
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000131956
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.99
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000035206
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:39.48
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194347035.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27372
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4511
 p-value of test no 14                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9928
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    3.47
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.96
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.26
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.99
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.46
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.52
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.48
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.68
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.01
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.14
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.52
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.14
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.98
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.76
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.10
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4854.85
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908189
   j =  2                              :            45898
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908590
   j =  2                              :            45702
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.88e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.42
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.98
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.09
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.88
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.03
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.40
 p-value of test no 124                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.53
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.55
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.16
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.93
 p-value of test no 135                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.49
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17205.71
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.29
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.73
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.98
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.20
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.43
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.43
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.28
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.10
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.66
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.54
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.74
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.79
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.84
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.63
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.43
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.61
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.48
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.45
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.16
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.95
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.12
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.40
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.57
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.08
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.84
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.03
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.05
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.61
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.84
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.10
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.23
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.57
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.26
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.81
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.51
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.87
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.15
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.57
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.28
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.34
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.11
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11502.62
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.03
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000011674
 
 Normal statistic for number of bits   :   0.092
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.48
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000034273
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:28.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195330075.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27373
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    3.52
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 29                 :    0.9945
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.28
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.67
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.81
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.40
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.22
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.65
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.40
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.41
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.25
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.06
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.70
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.56
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.82
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.74
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4917.75
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908175
   j =  2                              :            45908
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46246
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870246
   j =  1                              :        399907509
   j =  2                              :            46244
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 108                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.36
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.03
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.67
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.26
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.54
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.92
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.75
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.10
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.92
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.79
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.19
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.05
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.68
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.88
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.42
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.39
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.37
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.26
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.49
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.09
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.89
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.04
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.93
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.57
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.31
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.97
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.31
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.15
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.27
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.87
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.51
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.49
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.35
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.77
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.55
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.39
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.20
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.88
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.07
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.28
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.49
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5088.01
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.44
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.98
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.11
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.63
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.17
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.70
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999889208
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.57
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000064915
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:57.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196345883.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27374
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.40
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.48
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.23
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.20
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.22
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.07
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.09
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7281.62
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.31
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.61
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.23
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.76
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.90
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908382
   j =  2                              :            45803
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908543
   j =  2                              :            45724
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.09
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.28
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.95
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.93
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.99
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.21
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.27
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   64.74
 p-value of test no 146                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.13
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.32
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.48
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.09
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.01
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.36
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.10
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.49
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.76
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.89
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.27
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.08
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.28
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.56
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.65
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.55
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.84
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.74
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.39
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.10
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.17
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.91
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.32
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.85
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.52
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.53
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.96
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.02
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.61
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.79
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.92
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.32
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.45
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4669.97
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.65
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.23
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.89
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.43
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.50
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999924191
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.81
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999903818
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 241                :    0.9912
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:28.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197361691.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27375
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.99
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.40
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.99
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.79
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.79
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.58
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.05
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.24
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.50
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.35
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.76
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.15
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5230.11
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45698
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869698
   j =  1                              :        399908608
   j =  2                              :            45690
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907898
   j =  2                              :            46042
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.23
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.05
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.99
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.19
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.15
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.74
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.96
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.20
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.064
 p-value of test no 135                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.50
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.99
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.99
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.21
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.94
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.27
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.10
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.01
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.52
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.38
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.26
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.18
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.04
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.13
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.46
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.18
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.44
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.07
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.25
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.05
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.75
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.57
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.15
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.47
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.34
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.00
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.26
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.21
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.80
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.97
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 195                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.32
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.78
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.45
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.61
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.51
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 213                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10260.23
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.86e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.66
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.88
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.27
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.26
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.79
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.05
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.76
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000091192
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.28
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999848648
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 236                :  3.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.94
 p-value of test no 237                :  1.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.67
 p-value of test no 238                :  3.8e-3
 
 Sample variance                       :    0.11
 p-value of test no 239                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 240                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.69
 p-value of test no 243                :  3.6e-3
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:25.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198344731.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27376
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5290
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.17
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.01
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.48
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.15
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.87
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.78
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.42
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.12
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.01
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.14
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.21
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 62                 :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.54
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.11
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.50
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.51
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908493
   j =  2                              :            45746
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908593
   j =  2                              :            45702
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.10
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.97
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.77
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.41
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.26
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.71
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.64
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.45
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.70
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.52
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17114.92
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.23
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.22
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.12
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.91
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.26
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.92
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.92
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.57
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.34
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.85
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.78
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.07
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.34
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.29
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.23
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.79
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.03
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.03
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.72
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.04
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.92
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.19
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.04
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.38
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.36
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.90
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.92
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.18
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.04
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.25
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.31
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.55
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.34
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.48
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.52
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.98
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.08
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12065.71
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.32
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999944420
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.29
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999955277
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:30.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199360539.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27377
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7102
 p-value of test no 20                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.73
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.34
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.68
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.02
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.77
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.84
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.88
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7285.60
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.51
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.24
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.03
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.69
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908718
   j =  2                              :            45635
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908504
   j =  2                              :            45739
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.05
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.08
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.83
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.78
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.63
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.24
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.76
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.04
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.74
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.74
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17716.69
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.61
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.47
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.61
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.40
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.20
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.16
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.94
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.55
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.63
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.02
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.67
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.63
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.81
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.97
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.90
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.56
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.24
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.45
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.80
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.02
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.37
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.91
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.18
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.74
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.05
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.74
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.38
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.04
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.55
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.31
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.48
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.81
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.12
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.81
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4738.65
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.55
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.08
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3897.32
 p-value of test no 228                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.15
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.37
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999999947
 
 Normal statistic for number of bits   : -4.19e-4
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.65
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999971312
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 251                :    0.9933
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:41.60
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200376347.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27378
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    3.98
 p-value of test no 38                 :  8.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.96
 p-value of test no 41                 :  3.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.75
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.68
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.15
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.34
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.61
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.81
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.42
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.50
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.25
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.79
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.06
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.75
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908519
   j =  2                              :            45727
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908439
   j =  2                              :            45770
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-3
 p-value of test no 97                 :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.97
 p-value of test no 119                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.79
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.92
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.42
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.41
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.65
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.22
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.80
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.55
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.03
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.11
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.33
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.47
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.83
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.64
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.86
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.37
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.75
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.77
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.18
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.35
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.35
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.52
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.03
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.31
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.69
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.92
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.33
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.59
 p-value of test no 169                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.36
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.85
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.74
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.15
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.93
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.99
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.49
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.20
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.53
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.16
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.31
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 213                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9674.97
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 221                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.17
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.51
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.76
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.99
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.04
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.42
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.59
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999808526
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.70
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000057643
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:42.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201392155.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27379
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.59
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.43
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.56
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.95
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.81
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.57
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1540.88
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.83
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.12
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 63                 :    0.9932
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.01
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.04
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.42
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908725
   j =  2                              :            45636
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45614
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908774
   j =  2                              :            45610
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.80
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.11
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.92
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.13
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.63
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.23
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.86
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.82
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.45
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.16
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.70
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.18
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.35
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.75
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.42
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.53
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.48
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.60
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.76
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.06
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.42
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.62
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.11
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.52
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.42
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.26
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.11
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.71
 p-value of test no 166                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.82
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.86
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.51
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.18
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.77
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.03
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.91
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.30
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.55
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.80
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.52
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 180                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 182                :  7.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.48
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.78
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.72
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.74
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.07
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.05
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.74
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.80
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.26
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.21
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.71
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.65
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999977519
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.39
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000013444
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    2.36
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:10.31
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202506267.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27380
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 9                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5285
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9953
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.59
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.80
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.20
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.50
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.03
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.51
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.72
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.34
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7219.29
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.43
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.36
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.74
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.96
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.68
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908317
   j =  2                              :            45840
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45432
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869432
   j =  1                              :        399909136
   j =  2                              :            45432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.22
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.64
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.03
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.08
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.12
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.55
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.43
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.69
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17531.68
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.85
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.63
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.57
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.81
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.38
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.31
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.20
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.60
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.66
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.08
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.50
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.30
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.88
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.80
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.92
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.04
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.63
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.85
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.18
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.77
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.08
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5248.05
 p-value of test no 168                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.36
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.66
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.52
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.12
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.58
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.19
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.12
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.78
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.34
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.36
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.04
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.28
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.54
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.13
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.13
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.29
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.69
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.99
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000139324
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.62
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000091360
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:07.82
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183894044.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27381
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 7                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5553
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7114
 p-value of test no 20                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    3.82
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.42
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.68
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.29
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.13
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.49
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.05
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.28
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.30
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.16
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.34
 p-value of test no 66                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.45
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.21
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45485
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869485
   j =  1                              :        399909036
   j =  2                              :            45473
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907894
   j =  2                              :            46050
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.58
 p-value of test no 119                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.57
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.63
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.75
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.44
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.12
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.38
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.19
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.09
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.98
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17774.14
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.35
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.59
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.51
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.78
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.98
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.92
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.79
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.79
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.84
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.12
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.75
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.05
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.18
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.51
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.53
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.63
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.04
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.07
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.81
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.51
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.85
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.48
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.69
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.76
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.11
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.33
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.43
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.15
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.90
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 205                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.81
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.84
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.98
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.37
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.13
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.75
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3905.98
 p-value of test no 228                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.24
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.62
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.00
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999898790
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.03
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000122782
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:12.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184647708.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27382
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.59
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.32
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.39
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.34
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.47
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.20
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.32
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.22
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.97
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.06
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.99
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.34
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908197
   j =  2                              :            45900
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908575
   j =  2                              :            45702
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.92
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.55
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.03
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.20
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.20
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.87
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.16
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17008.03
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.99
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.99
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.01
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.80
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.45
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.43
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.51
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.15
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.41
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.03
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.87
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.33
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.08
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.66
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.58
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.46
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.44
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.61
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.96
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.39
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.33
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.32
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.69
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.56
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.34
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.28
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.83
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.56
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.66
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.83
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.09
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.27
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.98
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.12
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.10
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.84
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.69
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.01
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999875057
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.12
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000124360
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:03.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185663516.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27383
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.58
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.21
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.82
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.83
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.37
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.66
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.92
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.16
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.92
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.45
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.19
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.15
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.46
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908611
   j =  2                              :            45693
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907860
   j =  2                              :            46064
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.23
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.71
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.69
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.14
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.44
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.78
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.68
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.13
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.94
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17324.09
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.28
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.34
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.21
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.56
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.53
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   73.85
 p-value of test no 152                :  1.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.99
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.39
 p-value of test no 154                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.94
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.10
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.03
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.68
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.02
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.26
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.04
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.90
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.82
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.12
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.62
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.23
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.66
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.43
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.70
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.11
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.76
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.50
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.64
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.73
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.45
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.52
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.01
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.88
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.38
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.50
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.52
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.13
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.24
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.92
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.33
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.65
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000011560
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.12
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000074956
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.064
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:32.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 M (L=50, r=25)      1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186908700.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27384
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.30
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.14
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.49
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.31
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.15
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.85
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.11
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.85
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.35
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.58
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.07
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.44
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.29
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.73
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46159
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907688
   j =  2                              :            46147
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908752
   j =  2                              :            45621
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.29
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.32
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.17
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.46
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.79
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.41
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.49
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.05
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.55
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.59
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.92
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.78
 p-value of test no 146                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.05
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.61
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.75
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.21
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.54
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.01
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.81
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.68
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.87
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.26
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.70
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.39
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.71
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.10
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.55
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.22
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.24
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.47
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.14
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.80
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.87
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.84
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.22
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.57
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.47
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4677.18
 p-value of test no 173                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.89
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.15
 p-value of test no 175                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   33.58
 p-value of test no 176                :  7.8e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.43
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.89
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.28
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.97
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.35
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.97
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.92
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5088.39
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.63
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.02
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.15
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11544.78
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.49
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000004480
 
 Normal statistic for number of bits   :   0.035
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.44
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999902234
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.036
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:16.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9995 
  80  LinearComp, r = 0               7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187891740.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27385
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5297
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.92
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.16
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.19
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.08
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.29
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.68
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.87
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.99
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.01
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.37
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.70
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.40
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.59
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.48
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907853
   j =  2                              :            46069
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908313
   j =  2                              :            45839
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.40
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.05
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.78
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.88
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.56
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.20
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.94
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.73
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.46
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.39
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17227.10
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.00
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.92
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.04
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.47
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.53
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.30
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.40
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.78
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.14
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.03
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.79
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.30
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.59
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.53
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.58
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.94
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.19
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.44
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.19
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.83
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.21
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.23
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.51
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.48
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.39
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.94
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.77
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.40
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.24
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.00
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.32
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.22
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.91
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.26
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.64
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.87
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.24
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11534.11
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.48
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.43
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999791741
 
 Normal statistic for number of bits   :   -1.65
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.53
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999932051
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 235                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    2.79
 p-value of test no 244                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:57.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188809244.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27386
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.65
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.06
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.68
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.56
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.38
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  286.01
 p-value of test no 54                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.53
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.99
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.60
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.89
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.93
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.74
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.01
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908107
   j =  2                              :            45945
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908421
   j =  2                              :            45785
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 95                 :    0.9989
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.90
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.26
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.42
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   13.89
 p-value of test no 122                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.05
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.52
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.12
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.60
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.03
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.63
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.64
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.81
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.98
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.39
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.09
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.36
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  186.10
 p-value of test no 159                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.60
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.67
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.21
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.44
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.28
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.70
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.50
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.10
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.51
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.19
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.90
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.96
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.95
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.16
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.98
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.29
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.90
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.12
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.03
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.09
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.49
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.23
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.05
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.84
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.09
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.74
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.04
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.09
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.39
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999864584
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.27
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999934922
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:07.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189693980.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27387
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.84
 p-value of test no 23                 :  1.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     344
 p-value of test no 37                 :  6.9e-3
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.15
 p-value of test no 41                 :  8.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.23
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.52
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.26
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.55
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.97
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.79
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  277.23
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.34
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.15
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.92
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.86
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.07
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.58
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.77
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908028
   j =  2                              :            45980
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907948
   j =  2                              :            46014
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.74
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.51
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.39
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.19
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.74
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.53
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.26
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.99
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.44
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.43
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.96
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.71
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.82
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.35
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.39
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.25
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.71
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.47
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  201.20
 p-value of test no 157                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.88
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.59
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.04
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.15
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.28
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.51
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.82
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.85
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.60
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.60
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.96
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.94
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.91
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.24
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.11
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.62
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.47
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.25
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.20
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.16
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.05
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.75
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.38
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.71
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.18
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.46
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.67
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11423.57
 p-value of test no 230                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.03
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000048772
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.12
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999860303
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:20.34
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190906396.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27388
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.69
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.88
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.58
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.76
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.40
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.50
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.33
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.70
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.78
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.42
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.40
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.77
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.12
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.14
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.71
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908558
   j =  2                              :            45715
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.59
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.52
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.96
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.17
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.78
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.05
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.92
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.62
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.95
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17041.35
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.28
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.58
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.07
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.28
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.13
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.24
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.55
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.10
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.75
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.93
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.76
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.27
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.30
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.58
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.39
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.60
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.52
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.61
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.72
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.53
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.85
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.91
 p-value of test no 170                :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.94
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.30
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.24
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.35
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.98
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 180                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.16
 p-value of test no 189                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.75
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.54
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.79
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.78
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.59
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.82
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.35
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.39
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.60
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.40
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.11
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000017395
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999914246
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:06.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192020508.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27389
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7085
 p-value of test no 15                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     837
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.97
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.72
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.91
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.84
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.52
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.84
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.67
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.23
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.74
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.75
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.40
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.68
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.92
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.24
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.67
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.24
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46300
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870300
   j =  1                              :        399907405
   j =  2                              :            46290
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908709
   j =  2                              :            45641
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-3
 p-value of test no 104                :    0.9983
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.80
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.22
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.29
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.68
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.43
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.00
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.15
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.04
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.36
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.087
 p-value of test no 135                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.67
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 142                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 144                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18008.70
 p-value of test no 145                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.02
 p-value of test no 146                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.63
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.74
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.10
 p-value of test no 152                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.13
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.39
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.66
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.48
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.47
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.95
 p-value of test no 161                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.03
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.33
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.40
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.89
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.25
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4776.29
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.47
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.06
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.68
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.62
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.43
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.83
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.83
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.23
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.66
 p-value of test no 177                :    0.9961
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.49
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.37
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.96
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.73
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
 p-value of test no 213                :    0.9978
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 214                :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9540.79
 p-value of test no 215                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.37
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.49
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.87
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3889.89
 p-value of test no 228                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.22
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.64
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.80
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999885077
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.21
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999927782
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:29.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  91  HammingWeight2, r = 27          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192970780.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27390
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.80
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.57
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.64
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.54
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.42
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.46
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.56
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.55
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.11
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.87
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.46
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.66
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.45
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.71
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.31
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.90
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908312
   j =  2                              :            45841
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908017
   j =  2                              :            45987
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.68
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.26
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.87
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.24
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.93
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 130                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.95
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.15
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.69
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.26
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.83
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.19
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.07
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.24
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.37
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.96
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.43
 p-value of test no 153                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.78
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.69
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.53
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.30
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.01
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.93
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.12
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.38
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.26
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.14
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.23
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.02
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.42
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.05
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.46
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.62
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.03
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.05
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.72
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.81
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.24
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.19
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.92
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.94
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.21
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.25
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.71
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.53
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.47
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.66
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.67
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.03
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.36
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.81
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000092869
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999993011
 
 Normal statistic for number of bits   :  -0.055
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:05.72
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193921052.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27391
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1242
 p-value of test no 11                 :    0.9996    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334362
   j =  1                              :        599997516
   j =  2                              :             1242
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    3.13
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.35
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.77
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.82
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.99
 p-value of test no 51                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.28
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.39
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.95
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.22
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.46
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.86
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.45
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.06
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.09
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.54
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908421
   j =  2                              :            45782
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907611
   j =  2                              :            46193
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 94                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 100                :  7.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 101                :    0.9901
 
 Anderson-Darling statistic = A2       :    8.13
 p-value of test no 102                :  1.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.01
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.28
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.07
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.80
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.47
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.14
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.36
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 127                :    0.9933
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.29
 p-value of test no 129                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.34
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.25
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.62
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.80
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.13
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.82
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.64
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.57
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.96
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.86
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.41
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.07
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.41
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.55
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.57
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.39
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.63
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.61
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.20
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.58
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.47
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.14
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.18
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.05
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.65
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.93
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.00
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.43
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.86
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.71
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.12
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.09
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.91
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.03
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.15
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.13
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5076.56
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.63
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.30
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.56
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.27
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.91
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.10
 p-value of test no 231                :  8.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999909602
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.19
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999966704
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:27.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9996 
  50  SampleProd, t = 8               1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194871324.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27392
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.22
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.73
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.91
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.96
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.22
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.81
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.52
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.63
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.28
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.26
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.15
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.60
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.05
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.12
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.58
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908553
   j =  2                              :            45719
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908091
   j =  2                              :            45950
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 86                 :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.55
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.17
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.47
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.86
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.96
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.47
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.21
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 132                :    0.9990
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.55
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.56
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 143                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17068.34
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.51
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.35
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.16
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.04
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.71
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.19
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.79
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.10
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.85
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.95
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.30
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.59
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.81
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.62
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.50
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.55
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.54
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.83
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.42
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.46
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.53
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.60
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.05
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.65
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.97
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.06
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.58
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.29
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.92
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.58
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.37
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.58
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.38
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.77
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.57
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.88
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.43
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.49
 p-value of test no 218                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 221                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.07
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.26
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.08
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.15
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.07
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.35
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.04
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000033130
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.92
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000077713
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    2.00
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:02.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195854364.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27393
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 9                  :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.53
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.50
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.10
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.09
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.88
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.65
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.03
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.17
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.16
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.16
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.72
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.44
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.64
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908413
   j =  2                              :            45789
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908362
   j =  2                              :            45813
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.24
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.31
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.12
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.37
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.13
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.90
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.15
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.47
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.42
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.06
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.08
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.73
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.32
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.59
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.67
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.56
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.83
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.99
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.63
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.97
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.48
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.68
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.96
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.66
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.49
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.84
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.43
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.08
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4680.55
 p-value of test no 168                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.61
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.21
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.34
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.46
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.73
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.02
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.65
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.14
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.63
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.14
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.91
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.35
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.22
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.45
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.36
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.03
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4329.57
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.85
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.65
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.43
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000136003
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.24
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999963386
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:48.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9991 
  78  RandomWalk1 J (L=10000, r=0)    0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196837404.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27394
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 12                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.97
 p-value of test no 24                 :  9.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     834
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.47
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.31
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.63
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.01
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.20
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.69
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.23
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.35
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6843.15
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.20
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.25
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.74
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5202.06
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46352
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870352
   j =  1                              :        399907299
   j =  2                              :            46346
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908339
   j =  2                              :            45826
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 78                 :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  4.0e-3
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 95                 :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.50e-4
 p-value of test no 110                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 118                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.31
 p-value of test no 119                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.59
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.42
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.38
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.02
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.44
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.22
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.86
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.34
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.84
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.02
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.48
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.59
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.13
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.09
 p-value of test no 156                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.78
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.87
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.73
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.59
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.71
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.42
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.08
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.16
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.53
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.60
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.59
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.59
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.97
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.46
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.22
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.94
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.88
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.24
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.58
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.46
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.39
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.68
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.90
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.84
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.49
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5067.96
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.90
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.29
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.23
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12096.87
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.08
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000012589
 
 Normal statistic for number of bits   :   0.100
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.02
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000040282
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:22.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197820444.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27395
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.37
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.12
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   92.92
 p-value of test no 50                 :  7.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.40
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.25
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.80
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.00
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.22
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.76
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.01
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.48
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.20
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.86
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  159.25
 p-value of test no 67                 :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.51
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908278
   j =  2                              :            45855
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 86                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.63
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.78
 p-value of test no 120                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.29
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.92
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.15
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.82
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.54
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.70
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.67
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.41
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17160.23
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.47
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.17
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.23
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.07
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.95
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.97
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.20
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.22
 p-value of test no 155                :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.06
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.85
 p-value of test no 157                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.49
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.97
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.16
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.13
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.28
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.35
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.74
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.78
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.93
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.60
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.11
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.78
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.20
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.06
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.20
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.26
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.08
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.43
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.30
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.06
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10331.45
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.64
 p-value of test no 216                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.75
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.49
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.51
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.16
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.39
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.69
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.02
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000012262
 
 Normal statistic for number of bits   :   0.097
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.17
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000086329
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:37.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          7.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198770716.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27396
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.07
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.72
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.72
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.79
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.78
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.34
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.08
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6802.35
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.98
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.03
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.83
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.88
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.69
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907939
   j =  2                              :            46026
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908455
   j =  2                              :            45768
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 88                 :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.21
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.64
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.33
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.01
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.56
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.97
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.21
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.25
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.07
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.18
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17243.43
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.96
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.04
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.34
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.55
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.68
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.77
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.17
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.31
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.72
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.35
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.01
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.57
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.28
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.23
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.72
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.64
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.01
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.03
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.32
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.18
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.33
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.64
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.39
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.10
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.33
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.58
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.60
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.94
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.87
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.50
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.53
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.43
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.00
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.76
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.57
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.01
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.93
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.58
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4266.30
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.76
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11567.92
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.39
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.27
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000036094
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.73
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999929822
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 236                :    0.9943
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:57.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199720988.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27397
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5315
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 39                 :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.81
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.29
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.17
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.76
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.06
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.05
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.96
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1551.09
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.59
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.45
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.78
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.60
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.53
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.50
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46221
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870221
   j =  1                              :        399907566
   j =  2                              :            46205
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908367
   j =  2                              :            45812
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-3
 p-value of test no 103                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 108                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.02
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.03
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.64
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.10
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.50
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.57
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.62
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.91
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.28
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.75
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.70
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.85
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.78
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.73
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.99
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.07
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.89
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.29
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.27
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.00
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.29
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.81
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.10
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.29
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.63
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.29
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.55
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.25
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.91
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.96
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.09
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.99
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.68
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.67
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.14
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.51
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.73
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.08
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.20
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.57
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.68
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.94
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.55
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.45
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9719.41
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.44
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.53
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.81
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.43
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.42
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.58
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.43
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.39
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000063346
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.74
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999917426
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:59.90
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200704028.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27398
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.19
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.62
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.70
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.96
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.32
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.72
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.02
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1320.37
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.29
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.23
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.92
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.85
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.72
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.95
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907855
   j =  2                              :            46071
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908418
   j =  2                              :            45785
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.49
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.08
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.46
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.77
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.79
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.86
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.97
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.50
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.63
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.50
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.47
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.91
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.15
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.63
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.50
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.75
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.28
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.15
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.55
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.86
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.38
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.95
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.78
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.77
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.81
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.10
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.61
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.70
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.55
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5238.30
 p-value of test no 168                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.23
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.65
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.71
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.92
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.31
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.26
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.21
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.17
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.13
 p-value of test no 189                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.21
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.73
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.06
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.00
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.87
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.96
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.86
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.45
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.78
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.66
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.06
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.42
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.54
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000126688
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.57
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000028222
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9972
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.028
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:42.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201719836.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27399
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.99
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.66
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.85
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.99
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.02
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.52
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.21
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.28
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.10
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.53
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.12
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.80
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4919.56
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907927
   j =  2                              :            46032
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46323
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870323
   j =  1                              :        399907357
   j =  2                              :            46317
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 84                 :  3.1e-3
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 85                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.24
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.74
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.86
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.21
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.42
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.44
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 126                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.86
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.79
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.64
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.29
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.90
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.03
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.25
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.87
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.36
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.95
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.96
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.24
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.12
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.65
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.07
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.76
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.41
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.23
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.14
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.52
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.98
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.91
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.47
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.71
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.29
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.51
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.12
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.41
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.33
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.94
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.97
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.57
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.74
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.75
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.24
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.99
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.98
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.20
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.92
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.64
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.96e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 220                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5097.55
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.06
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.46
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.03
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12277.09
 p-value of test no 229                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.65
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.52
 p-value of test no 231                :  7.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000177127
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.24
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000001858
 
 Normal statistic for number of bits   :   0.015
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:17.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202735644.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27400
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.73
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.03
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.84
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.24
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.97
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.55
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.64
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.45
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.38
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.06
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.62
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.87
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908930
   j =  2                              :            45529
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45468
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869468
   j =  1                              :        399909067
   j =  2                              :            45462
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.96
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.92
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.22
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.74
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.57
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.06
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.65
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.61
 p-value of test no 133                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.32
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.98
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17591.23
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.40
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.46
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.57
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.65
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.91
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.30
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.79
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.92
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.60
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.07
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.46
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.93
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.55
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.79
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.04
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.94
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.40
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.93
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.53
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.10
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.89
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.80
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.35
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.06
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.16
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.29
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.94
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.64
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.18
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.21
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.71
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.11
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.28
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.93
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.11
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.07
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.75
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.89
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.46
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.29
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.45
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000003559
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.73
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000013405
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    2.52
 p-value of test no 249                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:33.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183926813.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27401
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    3.59
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.16
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.40
 p-value of test no 49                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.39
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.65
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.73
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.53
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.87
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7245.07
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.93
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.86
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.55
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.65
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.49
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907997
   j =  2                              :            45991
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908462
   j =  2                              :            45766
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  4.0e-3
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 78                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-3
 p-value of test no 106                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.74
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.39
 p-value of test no 122                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.71
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.17
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.71
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.85
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.25
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.43
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17781.01
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.75
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.25
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.09
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.88
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.46
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.28
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.87
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.24
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.15
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.61
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.66
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.34
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.18
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.75
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.72
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.81
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.08
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.69
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.25
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.09
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.76
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.50
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.65
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.68
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.78
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.57
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.03
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.72
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.26
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.42
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.50
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.44
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.51
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.79
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5101.24
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.95
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3870.08
 p-value of test no 228                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.79
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.01
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.15
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000020425
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.10
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999909836
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.66
 
 Sample variance                       :    2.04
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.10
 
 Sample variance                       :    2.05
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:08.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 184352797.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27402
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 5                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 6                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 19                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    3.30
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.58
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.37
 p-value of test no 50                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.48
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.68
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.87
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.71
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.25
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.47
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.09
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.21
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.88
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.72
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.42
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908208
   j =  2                              :            45884
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908274
   j =  2                              :            45857
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.62
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.17
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.15
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.21
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.86
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.59
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.18
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.08
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.72
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.60
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.70
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.35
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.68
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.07
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.43
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.62
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.46
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.81
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.84
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.15
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.98
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.72
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.61
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.31
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.49
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.66
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.96
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.90
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.59
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.68
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.76
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.99
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.67
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.06
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.12
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.17
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.53
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.85
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.59
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.39
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 213                :    0.9938
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9702.21
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.62
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.48
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.36
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.08
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12162.10
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.62
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.39
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999967205
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.31
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000071596
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:15.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185171997.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27403
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    3.37
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.89
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.29
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.63
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.06
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.85
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.39
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7270.82
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.46
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.53
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.58
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4776.85
 p-value of test no 68                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45511
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869511
   j =  1                              :        399908982
   j =  2                              :            45503
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908039
   j =  2                              :            45973
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.40
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.85
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.57
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.42
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.44
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.00
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.39
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.95
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.76
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.29
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.12
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.68
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.33
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.45
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.99
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.74
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.09
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.11
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.50
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.77
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.94
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.60
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.97
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.21
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.98
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.22
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.31
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.64
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.45
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.02
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.52
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.32
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.83
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.66
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.28
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.13
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.70
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.91
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.88
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.59
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.069
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.63
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.53
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.09
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.71
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.04
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.48
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.77
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.77
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.50
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.45
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.98
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000023431
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.26
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999945332
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.072
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:29.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186286109.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27404
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 11                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7584
 p-value of test no 19                 :  1.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    2.72
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.07
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.13
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.10
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.43
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.89
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.73
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.21
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.83
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.42
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.20
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.38
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.37
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.71
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46250
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870250
   j =  1                              :        399907505
   j =  2                              :            46240
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908436
   j =  2                              :            45779
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-4
 p-value of test no 112                :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.24
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.10
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.78
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.29
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.38
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.41
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.37
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.050
 p-value of test no 135                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.18
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17641.90
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.73
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.79
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.72
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.22
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.96
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.00
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.05
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.71
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.67
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.11
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.93
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.75
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.54
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.84
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.81
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.57
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.09
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.93
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.55
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.39
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.40
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.46
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.93
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4814.89
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.45
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.70
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.13
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.44
 p-value of test no 179                :  7.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.91
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.21
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.15
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.42
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.85
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.86
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.59
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.20
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.45
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.24
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.95
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999980384
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.82
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999879302
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.047
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:55.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187400221.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27405
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 8                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.98
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.00
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.99
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.58
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.05
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  362.00
 p-value of test no 55                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.61
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.05
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.11
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.99
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.76
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.00
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.06
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908381
   j =  2                              :            45808
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908711
   j =  2                              :            45640
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.83
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.71
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.06
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.62
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.96
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.76
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.13
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.27
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.90
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.41
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.97
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.25
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.37
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.33
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.61
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.34
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.80
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.23
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.35
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.39
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.99
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.11
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.39
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.84
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.22
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.85
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.58
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.67
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.39
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.82
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.30
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.23
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.73
 p-value of test no 169                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.73
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.55
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.14
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4827.79
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.24
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.17
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.98
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.54
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.60
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.85
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.73
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.50
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.74
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.09
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.15
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11495.95
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.60
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.85
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000160501
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.71
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000039028
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 235                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:25.61
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188940317.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27406
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.06
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.99
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.13
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.01
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.49
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.99
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.60
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.82
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.06
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.92
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.53
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.63
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.53
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907801
   j =  2                              :            46095
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908725
   j =  2                              :            45636
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 78                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 116                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.28
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.17
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.26
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.02
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.44
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.10
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.83
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.49
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.55
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.69
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.29
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17258.19
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.19
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.66
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.22
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.00
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.01
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.02
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.86
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.60
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.00
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.35
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.52
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.29
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.20
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.37
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.38
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.00
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.87
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.08
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.78
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.80
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.22
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.11
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.67
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.84
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.13
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.69
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.43
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9948
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.25
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.83
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.52
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.12
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.30
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.36
 p-value of test no 218                :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.89
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.01
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.40
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.93
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.03
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12116.60
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.73
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000095293
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.47
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999964991
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.14e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:26.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  94  HammingCorr, L = 1200           3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190054429.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27407
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997243
   j =  2                              :             1377
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9926
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.26
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.17
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.29
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.32
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.14
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.10
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.13
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.21
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.98
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.94
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.87
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.50
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908741
   j =  2                              :            45625
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.77
 p-value of test no 115                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.09
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.66
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.15
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.77
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.03
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.19
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.34
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-4
 p-value of test no 127                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.04
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.90
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.69
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.56
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.51
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.34
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.07
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.71
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.68
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.24
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.63
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.37
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.46
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.58
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.75
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.82
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.93
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.42
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.09
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.49
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.69
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.55
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.91
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.33
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.74
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.42
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.48
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.04
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.68
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.57
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.97
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.74
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.04
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.26
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.14
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.27
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.08
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.79
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.06
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.81
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.52
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.39
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.45
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.08
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.47
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.48
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999860561
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.98
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000018919
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 238                :    0.01
 
 Sample variance                       :    2.60
 p-value of test no 239                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:22.92
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191037469.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27408
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.75
 p-value of test no 29                 :  4.6e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.71
 p-value of test no 46                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.52
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.24
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.14
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.11
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.20
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.47
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.64
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.40
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.58
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.70
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.21
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.41
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.03
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.89
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.66
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.46
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907604
   j =  2                              :            46192
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908519
   j =  2                              :            45736
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.28
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.37
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.18
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.04
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.18
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.86
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.96
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.54
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.67
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.53
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.39
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.12
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.75
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.79
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.77
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.13
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.04
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.27
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.78
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.76
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.64
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.98
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.21
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.84
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.74
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.35
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.84
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.71
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.55
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.39
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.15
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.91
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.24
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.48
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.33
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.88
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.02
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.25
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.04
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.39
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.29
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.00
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.38
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.52
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9761.17
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.84
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.77
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.61
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.85
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.15
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.75
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.86
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.01
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000009919
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.37
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000059740
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP, t = 5           4.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192053277.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27409
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5611
 p-value of test no 13                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.57
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    3.23
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.35
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.42
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.28
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.24
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.38
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.84
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.30
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7186.10
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.63
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.02
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.07
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.23
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.79
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908364
   j =  2                              :            45812
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907711
   j =  2                              :            46137
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.40
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.07
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.99
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.97
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.00
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.83
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.06
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.66
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.50
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.30
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.64
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17168.21
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.21
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.36
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.84
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.67
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.30
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.21
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.99
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.42
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.53
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.25
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.28
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.14
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.55
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.66
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.98
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.67
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.17
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.24
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.36
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.46
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.27
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.28
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.49
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.84
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.67
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.79
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.69
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.79
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.83
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.77
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.58
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.38
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.34
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.54
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.68
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.48
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10174.41
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.57
 p-value of test no 217                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.25
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.43
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.50
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.12
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.09
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.42
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.30
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999929060
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.90
 p-value of test no 233                :  8.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000220441
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:01.75
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193003549.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27410
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.96
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.64
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.77
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.59
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.70
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.59
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.33
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.64
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.10
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.96
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.69
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.47
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.09
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.30
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4884.60
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908021
   j =  2                              :            45979
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907853
   j =  2                              :            46069
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.41
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.91
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.69
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.19
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.93
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.92
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.57
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.46
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.31
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.29
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17684.93
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.78
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.02
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.92
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.81
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.52
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.11
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.25
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.37
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.56
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.54
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.43
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.43
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.89
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.77
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.72
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.28
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.73
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.11
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.52
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.57
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.33
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.37
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.75
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.64
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.65
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.01
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 200                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.60
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.69
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10287.41
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.65
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.08
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.98
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.40
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.72
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.78
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.57
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.51
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999955505
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.01
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000116425
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:50.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193986589.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27411
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5280
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    4.22
 p-value of test no 24                 :  6.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     989
 p-value of test no 25                 :  1.8e-3
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.78
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.42
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.65
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.65
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.89
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.72
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.49
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.00
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.31
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.30
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.83
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.17
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908627
   j =  2                              :            45685
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908442
   j =  2                              :            45779
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  8.2e-3
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 92                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.06
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.44
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.69
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.68
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.37
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.63
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.38
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.47
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.79
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.73
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17550.82
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.20
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.34
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.35
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.77
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.20
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.12
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.62
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.67
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.57
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.46
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.39
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.28
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.83
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.54
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.20
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.24
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.78
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.73
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.01
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.66
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.19
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.22
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.17
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.73
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.44
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.91
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.00
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.97
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.49
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.37
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.53
 p-value of test no 179                :    0.9943
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.72
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.48
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.16
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.01
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.77
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.78
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.10
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.17
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.49
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.62
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.70
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.03
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999985043
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.88
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999960398
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.06e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:10.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195002397.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27412
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.22
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.22
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.13
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.39
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.61
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.15
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.26
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.56
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.73
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.48
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.63
 p-value of test no 66                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.55
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.08
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46607
 p-value of test no 71                 :  3.5e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870607
   j =  1                              :        399906788
   j =  2                              :            46603
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 88                 :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.21
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.31
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.08
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.91
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.23
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.67
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.51
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.56
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.12
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.07
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.51
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.38
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.60
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.52
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.49
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.56
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.21
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.07
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.84
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.25
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.56
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.64
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.57
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.11
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.90
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.16
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.25
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.97
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.81
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.80
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.15
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.71
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.95
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.58
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.45
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.80
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 195                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.74
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
 p-value of test no 205                :    0.9970
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.28
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.16
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.39
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.31
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5092.26
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.65
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.96
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.64
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.41
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.09
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999986435
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.53
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999992849
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    2.09
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:41.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  45  CollisionPermut, r = 10         3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196018205.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27413
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.79
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.63
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.51
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.20
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.67
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.42
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.91
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.95
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1304.65
 p-value of test no 56                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.59
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.30
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.07
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.20
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.27
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.33
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908655
   j =  2                              :            45665
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908154
   j =  2                              :            45920
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 98                 :    0.9915
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.17
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.27
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.80
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.45
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.81
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.43
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.09
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.64
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.54
 p-value of test no 147                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.12
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.45
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.59
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.67
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.88
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.08
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.80
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.33
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.02
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.71
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.57
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.03
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.71
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.65
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.81
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.81
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.15
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.38
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.14
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.33
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.37
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.37
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.83
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.94
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.89
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.41
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.54
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
 p-value of test no 181                :    0.9978
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.35
 p-value of test no 183                :    0.9906
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9975
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.57
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.92
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.60
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.39
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.87
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.33
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.21
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4704.36
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.14
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.16
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.77
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.61
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.00
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000076012
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.71
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999930260
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:53.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197099549.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27414
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.10
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.55
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.37
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.47
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.33
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.63
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.15
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.19
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.19
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.69
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.00
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.40
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.74
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.57
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.15
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.19
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908002
   j =  2                              :            45996
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908396
   j =  2                              :            45799
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.95
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.54
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.23
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.88
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.19
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.23
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.58
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.35
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9910
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.81
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.11
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.28
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.58
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17614.60
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.77
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.13
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.30
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.19
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.42
 p-value of test no 150                :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.36
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.36
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.23
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.22
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.66
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.97
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.88
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.64
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.21
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.34
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.30
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.03
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.87
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.15
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.53
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.81
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.76
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.71
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.34
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.43
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.98
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.85
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.33
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.65
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.40
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.95
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.51
 p-value of test no 217                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.26
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.80
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.14
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.96
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11590.46
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.22
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999936077
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.28
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000160636
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:16.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198148125.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27415
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7566
 p-value of test no 19                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.83
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.06
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.13
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.67
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.25
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.37
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.70
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.20
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.69
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7080.99
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.00
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.91
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.00
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.78
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5286.59
 p-value of test no 68                 :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908345
   j =  2                              :            45817
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46250
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870250
   j =  1                              :        399907505
   j =  2                              :            46240
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 87                 :    0.9927
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.31
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.44
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.61
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.95
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.79
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.39
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.82
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.75
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 139                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 140                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  179.70
 p-value of test no 141                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.37
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.94
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.87
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.93
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.51
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.39
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.73
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.07
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.34
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.86
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.76
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.03
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.85
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.13
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.69
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.15
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.45
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.35
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.99
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.78
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.05
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.47
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.92
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.26
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.18
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.57
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.38
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.27
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.21
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.19
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.41
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.88
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.07
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.70
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.44
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.60
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.48
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.71
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.86
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.85
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000034165
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.06
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000061273
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:34.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199196701.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27416
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.22
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.74
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.45
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.84
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.94
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.46
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.55
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.23
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.46
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.02
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 63                 :  2.3e-3
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.32
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.80
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.74
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.62
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908272
   j =  2                              :            45861
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45603
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869603
   j =  1                              :        399908799
   j =  2                              :            45593
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.81
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.76
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.23
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.90
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.35
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.98
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.24
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.72
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.33
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.42
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.04
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.82
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.02
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.58
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.43
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.29
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.10
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.78
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.11
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.41
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.33
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.83
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.20
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.57
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.83
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.81
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.21
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.22
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.66
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.59
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.21
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.39
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.69
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.03
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.07
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.75
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.48
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.11
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.06
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.27
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.87
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.63
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.74
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.34
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.97
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.32
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.15
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.34
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000061525
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.85
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000188008
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    2.24
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:27.56
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200212509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27417
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.72
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9924
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    3.91
 p-value of test no 44                 :  9.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.14
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.14
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.02
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.46
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.72
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.92
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.96
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7241.12
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.47
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.63
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.28
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.36
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.47
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908202
   j =  2                              :            45896
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908758
   j =  2                              :            45615
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 91                 :    0.9929
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.56
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.84
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.30
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.67
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.22
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.04
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.75
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-5
 p-value of test no 127                : 1 -  1.3e-5    *****
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 128                :  8.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.07
 p-value of test no 129                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.69
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.35
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.74
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17608.87
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.41
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.67
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.98
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.20
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.31
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.29
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.54
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.80
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.42
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.58
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.17
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.11
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.88
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.62
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.39
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.69
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.02
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.87
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.19
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.49
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.68
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.48
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.17
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.96
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.82
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.99
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.29
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.09
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.70
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.95
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.97
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.47
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.46
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.42
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-3
 p-value of test no 224                :    0.9978
 
 Anderson-Darling statistic = A2       :    4.83
 p-value of test no 225                :  3.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4595.07
 p-value of test no 226                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.00
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.09
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.70
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11558.86
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.76
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999929042
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.27
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000102745
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.94e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    2.17
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:23.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201228317.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27418
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 11                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.43
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.39
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.61
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.84
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.50
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  305.03
 p-value of test no 54                 :  9.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.83
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.09
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.68
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.76
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.32
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.81
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.13
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907737
   j =  2                              :            46127
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908198
   j =  2                              :            45898
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 90                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 92                 :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 105                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.62
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.75
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.94
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.65
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.00
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.19
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.50
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.21
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17126.93
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.01
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.66
 p-value of test no 147                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.74
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.79
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.00
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.21
 p-value of test no 153                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.05
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.05
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.37
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.20
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  583.73
 p-value of test no 158                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.67
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.15
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.24
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.62
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.84
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.58
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.42
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.20
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.16
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.55
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.24
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.55
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.23
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.13
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.87
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.44
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.81
 p-value of test no 179                :  2.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.43
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.99
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.44
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.66
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.83
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.79
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.23
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.10
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.16
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11546.46
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.92
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000097675
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.94
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000088297
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9995 
  34  Gap, r = 0                      9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202244125.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27419
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.94
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.03
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.88
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.18
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.33
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.26
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.26
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.39
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.73
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.45
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.73
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.44
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.17
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.52
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5398.77
 p-value of test no 68                 :  2.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46247
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870247
   j =  1                              :        399907509
   j =  2                              :            46241
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908001
   j =  2                              :            45992
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.56
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.40
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.30
 p-value of test no 122                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.29
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.25
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.40
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.19
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.65
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.13
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.75
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.93
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.60
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.68
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.63
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.54
 p-value of test no 149                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.26
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.45
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.52
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.59
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.27
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.61
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.19
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.47
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.09
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.59
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.73
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.20
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.32
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.17
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.98
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.59
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.71
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.45
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.87
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.17
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.85
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.83
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.92
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.36
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.90
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.21
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.19
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
 p-value of test no 201                :    0.9973
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  151.12
 p-value of test no 203                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.58
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.75
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.44
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.39
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.28
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.10
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.58
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11522.17
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.51
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.91
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999932627
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.53
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000060484
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 238                :    0.47
 
 Sample variance                       :    2.10
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:55:57.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203259933.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27420
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.88
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.66
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.00
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.54
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.10
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.29
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.26
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.61
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.95
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.36
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.37
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.69
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.14
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.21
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.82
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907995
   j =  2                              :            45998
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908505
   j =  2                              :            45743
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.69
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.44
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.94
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.59
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.26
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.82
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.09
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.23
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.41
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.72
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17197.41
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.69
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.85
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.16
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.41
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.31
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.37
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.95
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.16
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.42
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.29
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.07
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.57
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.07
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.29
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.88
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.31
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.64
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.95
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.32
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.56
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.65
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.87
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.24
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.04
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.24
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.26
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.83
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.85
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.40
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.04
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.06
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 201                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.55
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.96
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.65
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.42
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.49
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4731.56
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.49
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.24
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12116.90
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.06
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.48
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999973196
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.92
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000072949
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:35.75
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183959582.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27421
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 8                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7518
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.54
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.47
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.02
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.64
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.06
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.53
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.77
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.75
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.83
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.07
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.73
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.40
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908607
   j =  2                              :            45686
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908461
   j =  2                              :            45765
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 88                 :  8.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9966
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.14
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.56
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.70
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.89
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.29
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.29
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.78
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.79
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.91
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.71
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.45
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.49
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.16
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.56
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.08
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.03
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.22
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.35
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.98
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.85
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.13
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.04
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   89.33
 p-value of test no 162                : 1 -  6.2e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.79
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.94
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.27
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.79
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.63
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.79
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.45
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.74
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.70
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.94
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.22
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.53
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.65
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.84
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.06
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.52
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.58
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.18
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.60
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.40
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.28
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.39
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.30
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.61
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.95
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.31
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.89
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999900971
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.84
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000069196
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    2.08
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:00.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 M (L=1000, r=20)   1 -  6.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 183992350.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27422
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997435
   j =  2                              :             1281
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.18
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.25
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.03
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.83
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.84
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.62
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.78
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.97
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.03
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6847.85
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.22
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.51
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.52
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.84
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908061
   j =  2                              :            45965
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 101                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.77
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.54
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.71
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.20
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.87
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.06
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.58
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.05
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.16
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.58
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.88
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.81
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.14
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.32
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.97
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.84
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.73
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.88
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.61
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.39
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.25
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.83
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.25
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.73
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.00
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.38
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.01
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.86
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.82
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.19
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.42
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.36
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.63
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.93
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.28
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.85
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.01
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.24
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.65
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 204                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  259.91
 p-value of test no 207                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10296.72
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.61
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.89
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.70
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.78
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.14
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.18
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12055.03
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.87
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999936656
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.53
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999858047
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    2.07
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:56.19
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 185073694.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27423
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.01
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.07
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.58
 p-value of test no 49                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.22
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.62
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.01
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.51
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.17
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.87
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.17
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.88
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.27
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.45
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.82
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907871
   j =  2                              :            46054
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46217
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870217
   j =  1                              :        399907569
   j =  2                              :            46211
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.15
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.56
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.83
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.10
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.90
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.70
 p-value of test no 124                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.36
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.91
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.42
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.28
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17635.22
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.74
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.42
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.15
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.74
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.18
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.89
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.28
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.72
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.61
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.19
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.34
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.86
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.88
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.16
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.21
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.40
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.19
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.99
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.62
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.61
 p-value of test no 169                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.88
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.59
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.62
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.85
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.79
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.43
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.76
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.05
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
 p-value of test no 205                :    0.9973
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.79
 p-value of test no 207                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.92
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.49
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.74
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.72
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.49
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.81
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.78
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.56
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.60
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000113581
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.51
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999992831
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:39.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 186056734.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27424
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5630
 p-value of test no 13                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.72
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.64
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.78
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.61
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.48
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.50
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.46
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.11
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.42
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.00
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.73
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.73
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.53
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.12
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4924.64
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908204
   j =  2                              :            45886
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907825
   j =  2                              :            46083
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.50
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.37
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.56
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.46
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.60
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.28
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.78
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.67
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.81
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.43
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.99
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.77
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.16
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.36
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.76
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.58
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.31
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.89
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.16
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.05
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.27
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.97
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.76
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.84
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.07
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.28
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.36
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.58
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.02
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.20
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.69
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.72
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.89
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.83
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.53
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.07
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.46
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.83
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.14
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.74
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.71
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.03
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.67
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.18
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.79
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.62
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.86
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4295.83
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.68
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.17
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.17
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.71
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999952382
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.99
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000104410
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:50.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 187105310.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27425
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 9                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4503
 p-value of test no 16                 :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9971
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.59
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.40
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.65
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.03
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.90
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.77
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.36
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.20
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.95
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.94
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.45
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.64
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.01
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907934
   j =  2                              :            46030
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907840
   j =  2                              :            46074
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 100                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.65
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.49
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.44
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.68
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.03
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.82
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.52
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    4.42
 p-value of test no 140                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   95.19
 p-value of test no 141                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17731.91
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.89
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.95
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.48
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.41
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.67
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.89
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.06
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.53
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.86
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.76
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.65
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.90
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.97
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.51
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.87
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.08
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.73
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.49
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.03
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.32
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.81
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.67
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.78
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.00
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.65
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.19
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.04
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.56
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.61
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.36
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.12
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.94
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
 p-value of test no 208                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10312.99
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9789.15
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.90
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.36
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.94
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.74
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.18
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.46
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000165646
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.20
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999994085
 
 Normal statistic for number of bits   :  -0.047
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:17.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188088350.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27426
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 10                 :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    5.45
 p-value of test no 32                 :  1.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.55
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.76
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.09
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.25
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.34
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.49
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.85
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.52
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.39
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7245.84
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.63
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.96
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.49
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.75
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908182
   j =  2                              :            45906
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908495
   j =  2                              :            45748
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  8.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.61
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.60
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.86
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.66
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.78
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.12
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.56
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.37
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17434.31
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.88
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.76
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.44
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.86
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.21
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.81
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.61
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.10
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.09
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.40
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.80
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.86
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.18
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.11
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.88
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.24
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.00
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.27
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.99
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.51
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  302.70
 p-value of test no 167                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.64
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.29
 p-value of test no 169                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.53
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.92
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.24
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.54
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.70
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.42
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.76
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.25
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.62
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.25
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.82
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.19
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.51
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.29
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 223                :  1.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 225                :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4641.32
 p-value of test no 226                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.89
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.68
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.75
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.28
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.95
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999956372
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.53
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000012685
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.080
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:14.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 M (L=10000, r=0)    0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189071390.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27427
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    4.21
 p-value of test no 27                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.97
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.97
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.42
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.55
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.66
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.72
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.52
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.06
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.89
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.22
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.73
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908850
   j =  2                              :            45569
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908634
   j =  2                              :            45677
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.78
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.62
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.12
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.87
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.07
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.50
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.80
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.31
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.088
 p-value of test no 135                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.87
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.84
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.61
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.92
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.63
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.04
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.68
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.97
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.23
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.43
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.45
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.01
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.90
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.38
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.72
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.46
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.92
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  481.92
 p-value of test no 167                :  4.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.90
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.37
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.52
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.23
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.28
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.66
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.31
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.97
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.04
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.72
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.66
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.51
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.52
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4730.77
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.79
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.31
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.59
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.07
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.26
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.31
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000055774
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.92
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000030682
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    2.28
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:28.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 M (L=10000, r=0)    4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190185502.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27428
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.47
 p-value of test no 40                 :  5.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.03
 p-value of test no 46                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.86
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.25
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.74
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.00
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.54
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.09
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.38
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.51
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.62
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.45
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.74
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908471
   j =  2                              :            45757
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908659
   j =  2                              :            45663
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.12
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.61
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.59
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.49
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.44
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.53
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.17
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.15
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.75
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.95
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.02
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.97
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.16
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.82
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.79
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.21
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.10
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.86
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.72
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.46
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.77
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.59
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.61
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.30
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.01
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.02
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.47
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.02
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.92
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.98
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.30
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.90
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.48
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.49
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.26
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.02
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.95
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.04
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.93
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.65
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.76
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.54
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.65
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.56
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.54
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.84
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.21
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.50
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999987698
 
 Normal statistic for number of bits   :  -0.097
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.82
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999918656
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:14.92
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191201310.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
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                     Run no 27429
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 5                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.10
 p-value of test no 28                 :  8.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    3.49
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.47
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.71
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.11
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.59
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.51
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.57
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.37
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.26
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.92
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.69
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.21
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.13
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.81
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907738
   j =  2                              :            46119
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908384
   j =  2                              :            45802
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.76
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.90
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.43
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.33
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.47
 p-value of test no 125                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.88
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.48
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.21
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.27
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.10
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.41
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.30
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.51
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.42
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.87
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.76
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.29
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.68
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.29
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.05
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.70
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.81
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.33
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.75
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.37
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.96
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.44
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.98
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.22
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.28
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.28
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.95
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.50
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.27
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.28
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.46
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.91
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.38
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.33
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.48
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.44
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.49
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.71
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.06
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.47
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.80
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.94
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.23
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.73
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999857855
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.90
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000116374
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9950
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:36.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192151582.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27430
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.64
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.52
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.99
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.02
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.45
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.38
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.82
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.79
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.68
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.75
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.79
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.39
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.37
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908104
   j =  2                              :            45942
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908827
   j =  2                              :            45582
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.51
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.06
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.05
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.05
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.70
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.57
 p-value of test no 125                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.94
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.50
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.73
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17820.75
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.99
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.13
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.78
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.02
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.79
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.26
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.28
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.68
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.45
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.90
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.86
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.45
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.03
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.47
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.42
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.97
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.30
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.37
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.19
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.77
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.96
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.25
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.02
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.94
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.86
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.95
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.07
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.03
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.99
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.46
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 180                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 182                :  6.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 183                :    0.9923
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.41
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.37
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.72
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9908
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.47
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.33
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.35
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.10
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.67
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.20
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.91
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.61
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000093487
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000135784
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 251                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:27.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193134622.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27431
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 4                  :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1494
 p-value of test no 11                 :  2.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334614
   j =  1                              :        599997012
   j =  2                              :             1494
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5217
 p-value of test no 13                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4573
 p-value of test no 14                 :  1.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.36
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.42
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.54
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.19
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.03
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.44
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.58
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.97
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.42
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.95
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.71
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.78
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4798.29
 p-value of test no 68                 :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908500
   j =  2                              :            45744
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 79                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
 p-value of test no 84                 :    0.9954
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.33
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.13
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.98
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.75
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.57
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.25
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.32
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.12
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.47
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.33
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.00
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.30
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.82
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.82
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.81
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.81
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.49
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.84
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.94
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.27
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.89
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.76
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.28
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.27
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.45
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.95
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.89
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.82
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.87
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.81
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.59
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.88
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.41
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.48
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.18
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.24
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.52
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.27
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.92
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.53
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.52
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.30
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.27
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.77
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.88
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.33
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.60e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.15
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.37
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.37
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.96
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.26
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.13
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.62
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000063730
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.21
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000180361
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.073
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 250                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:18.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           2.8e-4
  14  BirthdaySpacings, t = 3         1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194248734.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27432
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.94
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.96
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.86
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.05
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.52
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.89
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.80
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.50
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.19
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.47
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.03
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4833.09
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908337
   j =  2                              :            45827
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908032
   j =  2                              :            45984
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 93                 :    0.9900
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.68
 p-value of test no 118                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.97
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.23
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.90
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.96
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.76
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.01
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.39
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.68
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.04
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.24
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.55
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.90
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.68
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.89
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.27
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.38
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.53
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.26
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.91
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.14
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.09
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.54
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.94
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.11
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.15
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.47
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.44
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.02
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.50
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.93
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.61
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.33
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.96
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.09
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.31
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.08
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.98
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.04
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.73
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.04
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.58
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.16
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.64
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4302.01
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4291.80
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.80
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.63
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.37
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000105022
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.84
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000123289
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -4.04e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:00:54.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195231774.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27433
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.59
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.93
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.99
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.22
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.67
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.65
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.23
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.15
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.66
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.16
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.90
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45488
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869488
   j =  1                              :        399909029
   j =  2                              :            45478
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908271
   j =  2                              :            45857
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.55
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.40
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.17
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.84
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.37
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.46
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 127                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.93
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.83
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.95
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.18
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.50
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.74
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.89
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.07
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.73
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.54
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.13
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.27
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.66
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.95
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.91
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.76
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.65
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.75
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.37
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.42
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.95
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.17
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.21
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.45
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.50
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.46
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.86
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.46
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.98
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.58
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.40
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.06
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 206                :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.13
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.40
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-4
 p-value of test no 212                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10354.66
 p-value of test no 215                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.35
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.59
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.63
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.85
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.28
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.98
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.30
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000111046
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.75
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000020959
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:53.26
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196214814.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27434
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.67
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.54
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.45
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.93
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.15
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.98
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.22
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.58
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.13
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.49
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.48
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.29
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.56
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.95
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.78
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.19
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907923
   j =  2                              :            46037
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46284
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870284
   j =  1                              :        399907436
   j =  2                              :            46276
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 90                 :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.71
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.40
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.60
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.97
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.24
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.30
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.50
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.15
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.06
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.13
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.95
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.63
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.57
 p-value of test no 150                :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   54.01
 p-value of test no 154                :  4.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.34
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.97
 p-value of test no 156                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.98
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.77
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.77
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.39
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.73
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.21
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.61
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.42
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.14
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.10
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.96
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.41
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.30
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.51
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.34
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.12
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.74
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.60
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.87
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.88
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
 p-value of test no 185                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.96
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.44
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.74
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.19
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.85
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5081.22
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.26
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.65
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.55
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.79
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.62
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.41
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999998159
 
 Normal statistic for number of bits   :  -0.015
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.71
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999949019
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.047
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.92e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:32.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      4.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197296158.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27435
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4507
 p-value of test no 14                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.55
 p-value of test no 48                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.31
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.34
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.38
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.11
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.09
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1301.34
 p-value of test no 56                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.87
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.37
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.75
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.64
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4843.61
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908421
   j =  2                              :            45788
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908276
   j =  2                              :            45862
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  1.0e-2
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 3.42e-4
 p-value of test no 113                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.79
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.06
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.25
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.05
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.20
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.46
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.46
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.69
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.28
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.62
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.70
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.80
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.49
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.48
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.97
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.60
 p-value of test no 150                :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.28
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.59
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.24
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.53
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.78
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.25
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.46
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.27
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.07
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.97
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.62
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.53
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.34
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.18
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.11
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.60
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.19
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.46
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.42
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.26
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.43
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.01
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.25
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.00
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.37
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.85
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.00
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.80
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.50
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.93
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.80
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.98
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.38
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.00
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11579.47
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11503.30
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.50
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999985490
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.07
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999935039
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 241                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 242                :  8.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.55
 p-value of test no 243                :  5.5e-3
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:41.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198279198.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27436
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5201
 p-value of test no 13                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.42
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.79
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.54
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.64
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.68
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.99
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.58
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.10
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.26
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.13
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.39
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.23
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.08
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46154
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870154
   j =  1                              :        399907696
   j =  2                              :            46146
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908148
   j =  2                              :            45920
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-4
 p-value of test no 112                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.38
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.83
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.58
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.89
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.60
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.55
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   68.45
 p-value of test no 129                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.80
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.29
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.80
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.21
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.43
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.88
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.10
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.17
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.12
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.43
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.74
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.96
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.73
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.66
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.58
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.40
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.34
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.99
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.34
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.57
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.69
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.46
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.20
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.63
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.28
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.87
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5216.19
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.07
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.19
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.86
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.58
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.73
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9789.15
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.68
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.77
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.02
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.39
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.65
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12188.31
 p-value of test no 229                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.37
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.24
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999862904
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.44
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999954365
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:51.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199295006.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27437
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5551
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    4.35
 p-value of test no 33                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.25
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.25
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.67
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.12
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.92
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.68
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.43
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.16
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.43
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.06
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.36
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.17
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.30
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4831.32
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45531
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869531
   j =  1                              :        399908941
   j =  2                              :            45525
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907739
   j =  2                              :            46120
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.52
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.86
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.97
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.01
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.45
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.78
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.98
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.16
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.96
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.27
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.69
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.02
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.07
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.59
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.56
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.72
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.71
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.08
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.22
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.73
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.70
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.68
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.26
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.56
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.36
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.17
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.66
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.00
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.94
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.06
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.51
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.80
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.61
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.89
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.42
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.64
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.39
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.39
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.47
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.31
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.30
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.52
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 209                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 210                :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10320.92
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.39
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5034.77
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.42
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.68
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.25
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12101.24
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.88
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.58
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999902996
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.69
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000012799
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.015
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:51.92
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200310814.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27438
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.56
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.69
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.11
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.03
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.48
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.76
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.09
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.31
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.75
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.89
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.30
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.03
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.20
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.63
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908701
   j =  2                              :            45645
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45525
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869525
   j =  1                              :        399908957
   j =  2                              :            45511
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.67
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.35
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.36
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.07
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.56
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.12
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17655.41
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.32
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.64
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.16
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.51
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.95
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.41
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.81
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.98
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.01
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.23
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.51
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.95
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.36
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.82
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.34
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.25
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.64
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.20
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.85
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.76
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.94
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.98
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.19
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.04
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.31
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.92
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.07
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.42
 p-value of test no 177                :  7.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.54
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.28
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.72
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.35
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.84
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.15
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.09
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.39
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.55
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.77
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.90
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11512.26
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.15
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.56
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999989138
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.76
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999914783
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:01.67
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201293854.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27439
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7553
 p-value of test no 19                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.49
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.38
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.26
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.90
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.62
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.81
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.11
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.89
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.36
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.60
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.02
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.06
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.31
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5164.91
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45403
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869403
   j =  1                              :        399909199
   j =  2                              :            45393
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908017
   j =  2                              :            45990
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 80                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.11
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.30
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.37
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.56
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.71
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.25
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.84
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.38
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.07
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.72
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.18
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.19
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.15
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.34
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.72
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.62
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.49
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.53
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.11
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.42
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.30
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.13
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.83
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.91
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.65
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.87
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.47
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.82
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.72
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.15
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.34
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.36
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.50
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.22
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.34
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.19
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.64
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
 p-value of test no 181                :    0.9989
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 183                :    0.9937
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.19
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.58
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.88
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.26
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.23
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.86
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.50
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.58
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.52
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.57
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.50
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.42
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000012751
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.12
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000024067
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.036
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:02.46
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202375198.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27440
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5298
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.18
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    3.15
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.81
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.61
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.55
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.26
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.72
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.50
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.96
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.68
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-4
 p-value of test no 58                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.68
 p-value of test no 59                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 60                 :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   58.67
 p-value of test no 61                 :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.44
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.75
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4900.90
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907749
   j =  2                              :            46118
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908510
   j =  2                              :            45739
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 115                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.31
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.91
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.44
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.03
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.77
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.78
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.45
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.57
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.62
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.31
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.80
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.42
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.32
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.81
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.68
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.21
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.75
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.26
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.63
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.01
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.41
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.35
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.01
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.70
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.11
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.58
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.77
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.00
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.92
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.77
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.80
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.18
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.95
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.06
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.50
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.54
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.97
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.39
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.36
 p-value of test no 176                :    0.9986
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.46
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.09
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.80
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.47
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.46
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.34
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.65
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.45
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.99
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.00
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11492.48
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.95
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.94
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000069571
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.06
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000003421
 
 Normal statistic for number of bits   :   0.027
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.88
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:18:15.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188874752.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27441
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.06
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.99
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.60
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.02
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.06
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.31
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.37
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.00
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.19
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.77
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.40
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.10
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.06
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.96
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.30
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.22
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908197
   j =  2                              :            45894
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908491
   j =  2                              :            45750
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.68
 p-value of test no 118                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.92
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.95
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.71
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.99
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.40
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.20
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.58
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.95
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.79
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17380.56
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.27
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.01
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.49
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.92
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.47
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.07
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.14
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.57
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.37
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.64
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  209.22
 p-value of test no 156                :  4.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.85
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.93
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.27
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.90
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.12
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.68
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.37
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.95
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.95
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.48
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.71
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.26
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.61
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.52
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.42
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.53
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.32
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.52
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.87
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.56
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.36
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.78
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.47
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.97
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5141.30
 p-value of test no 226                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.59
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.21
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.82
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.64
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.52
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999997094
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.65
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000059437
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:46.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190611479.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27442
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.88
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.52
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.42
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.84
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.29
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.55
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.09
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.59
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6935.87
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.63
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.11
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.88
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.31
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.73
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46184
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907635
   j =  2                              :            46178
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908382
   j =  2                              :            45806
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-3
 p-value of test no 104                :    0.9977
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.28
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.26
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.53
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.54
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.95
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.19
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.14
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.96
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.21
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.68
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.74
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.82
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.89
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.92
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.73
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.85
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.33
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.19
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.26
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.12
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.19
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.24
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.08
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.01
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.72
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.02
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.06
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.68
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.08
 p-value of test no 170                :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.46
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.08
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.27
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.83
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.03
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.55
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.55
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.14
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.03
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.29
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.28
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.64
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.40
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.01
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.08
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.90
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.21
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999999089
 
 Normal statistic for number of bits   : -7.20e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.20
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999894644
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 235                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:41.35
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191135767.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27443
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.22
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.39
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.22
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.11
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.14
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.36
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.44
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.16
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.09
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.90
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.44
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.97
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.45
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.28
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.26
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.49
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45490
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869490
   j =  1                              :        399909023
   j =  2                              :            45484
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46233
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870233
   j =  1                              :        399907537
   j =  2                              :            46227
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 100                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 116                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.73
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.11
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.53
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.03
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.42
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.92
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.26
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.69
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17602.85
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.43
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.56
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.05
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.33
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.94
 p-value of test no 151                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.87
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.76
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.73
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.74
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.87
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.72
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.55
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.23
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.95
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.83
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.01
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.59
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.94
 p-value of test no 166                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.92
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.22
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.70
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.41
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.85
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.87
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.67
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.85
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.56
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.12
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.67
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.83
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.23
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.48
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.34
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.91
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.68
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.85
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.01
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.31
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.63
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.05
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.82
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000001918
 
 Normal statistic for number of bits   :   0.015
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.32
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000097795
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.057
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.73
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:09.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192184343.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27444
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7552
 p-value of test no 15                 :  3.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.13
 p-value of test no 41                 :    0.9994    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.12
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.51
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.35
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.46
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.53
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.98
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.17
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.29
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.88
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.66
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.34
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.39
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.54
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.52
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908324
   j =  2                              :            45835
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907937
   j =  2                              :            46027
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 87                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.34
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.66
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.75
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.84
 p-value of test no 123                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.13
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.36
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.61
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.72
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17552.91
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.54
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.40
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.71
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.52
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.80
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.57
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.88
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.72
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.10
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.36
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.32
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.37
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.23
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.24
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.04
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.28
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.57
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.31
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.22
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.34
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.86
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.35
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.69
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.89
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.25
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.64
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.70
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.04
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.72
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.60
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.98
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.30
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.88
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.33
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.74
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.82
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4285.82
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.31
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11590.10
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.28
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000137200
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.93
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999757955
 
 Normal statistic for number of bits   :   -1.91
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:49.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP, t = 16          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193134615.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27445
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 11                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.39
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.37
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     118
 p-value of test no 43                 :    0.9961
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.57
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.39
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.60
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.01
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.87
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.92
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.68
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.73
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.72
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.15
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.28
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.72
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.57
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908175
   j =  2                              :            45899
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908350
   j =  2                              :            45819
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.68
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.77
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.80
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.55
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.33
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.37
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.56
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.32
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.11
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.11
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.13
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.56
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.02
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.17
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.05
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.60
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.15
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.73
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.34
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.12
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.20
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.83
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.13
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.09
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.14
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.26
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.77
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.22
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.00
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.78
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.62
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.10
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.06
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.74
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.79
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.14
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.30
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.24
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.05
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.86
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.20
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    3.10
 p-value of test no 189                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.50
 p-value of test no 196                :  5.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.11
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.79
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.66
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.38
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 213                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9709.06
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.86
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.59
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.19
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.38
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11623.57
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.64
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.92
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000076540
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.22
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000166072
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.18
 p-value of test no 254                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:57.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194183191.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27446
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 12                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    3.84
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.89
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.18
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.35
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.86
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.53
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.21
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.70
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.68
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.19
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.70
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.67
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.56
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5257.99
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908147
   j =  2                              :            45919
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907932
   j =  2                              :            46025
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.39
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.53
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.20
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.96
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.86
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.44
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.24
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.28
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.84
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.28
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.46
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.39
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.69
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.51
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.47
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.42
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.59
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.31
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.33
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.13
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.39
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.12
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.84
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.56
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.73
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.72
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.47
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.37
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.66
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.28
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.37
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.85
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.70
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.44
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.83
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.32
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.61
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.10
 p-value of test no 177                :    0.9990    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.77
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    2.14
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.32
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.38
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.96
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.40
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.46
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.05
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.63
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.74
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.57
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11582.91
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.91
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.99
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999995615
 
 Normal statistic for number of bits   :  -0.035
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.08
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000192439
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:09.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0               0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195723287.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27447
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5274
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.35
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.09
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.33
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.14
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.93
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.34
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.55
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.22
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.51
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.17
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.26
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.41
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.83
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-3
 p-value of test no 59                 :    0.9987
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 60                 :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.99
 p-value of test no 61                 :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.49
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.75
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.77
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907880
   j =  2                              :            46054
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908157
   j =  2                              :            45920
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.61
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.88
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.31
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.87
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.21
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.74
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.92
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.44
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.77
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.45
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.80
 p-value of test no 146                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.85
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.06
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.97
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.77
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.10
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.51
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.86
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.10
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.33
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.61
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.78
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.32
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.06
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.74
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.91
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.12
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.20
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.09
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.65
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.69
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.83
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.13
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.59
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.55
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.56
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.95
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.58
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.43
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.51
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.55
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.61
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.89
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.66
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.92
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.55
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.05
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.78
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.25
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12125.71
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.78
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.67
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999876161
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.38
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999935087
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:32.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196902935.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27448
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4495
 p-value of test no 14                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.08
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.43
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.82
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.98
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.50
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.66
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.15
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.67
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.01
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.31
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.84
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.21
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908261
   j =  2                              :            45868
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.53
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.39
 p-value of test no 122                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.36
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.75
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.18
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.54
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.25
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.39
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.94
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.02
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   75.53
 p-value of test no 146                :  1.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.04
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.67
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.91
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.54
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.24
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.50
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.76
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.85
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.81
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.24
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.46
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.27
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.50
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.67
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.41
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.86
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.70
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.32
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.79
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.63
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.86
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.44
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.60
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.85
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.27
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.54
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.04
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.50
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.29
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.49
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.33
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.56
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.80
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 214                :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9603.95
 p-value of test no 215                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.98
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.41
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.09
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.07
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.56
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.39
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.91
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999926135
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.12
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000039349
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:13.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198049815.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27449
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7491
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.85
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.24
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.71
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.07
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.84
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.22
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.58
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.28
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.81
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.59
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.48
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.98
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.58
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908252
   j =  2                              :            45868
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908314
   j =  2                              :            45840
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.11
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.09
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.68
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.26
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.08
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.35
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.59
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.83
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.45
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17241.56
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.51
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.20
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.64
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.31
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.66
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.39
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.09
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.39
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.66
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.13
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.94
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.34
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.70
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.03
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.25
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.91
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.52
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.67
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.30
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.79
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.62
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.74
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.84
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.43
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.20
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.38
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.19
 p-value of test no 184                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.99
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.35
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.98
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.71
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.51
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.70
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.23
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.59
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.74
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11584.74
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.65
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.53
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000139993
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.59
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999992402
 
 Normal statistic for number of bits   :  -0.060
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:03.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199000087.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27450
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.10
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.38
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.91
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.74
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.95
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.97
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.95
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.44
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.90
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.58
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.58
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45595
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869595
   j =  1                              :        399908810
   j =  2                              :            45595
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908047
   j =  2                              :            45969
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 77                 :    0.9938
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 111                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.25
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.38
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.09
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.42
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.58
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.01
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.62
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.83
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.28
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.97
 p-value of test no 148                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.71
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.07
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.55
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.60
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.10
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.45
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.89
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.43
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.41
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.84
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.25
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.09
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.10
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.41
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.20
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.47
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.70
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.62
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.26
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.43
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.42
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.08
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.99
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.54
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.53
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.17
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.90
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.74
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 201                :    0.9927
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.80
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.38
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10275.22
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.70
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.59
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 223                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5070.66
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.64
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.34
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.84
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.23
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.87
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999878810
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.28
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999968141
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:40.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199917591.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27451
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 16                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.78
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.04
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.25
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.48
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.02
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.48
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.88
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.30
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.09
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.01
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.41
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.35
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.96
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.67
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908352
   j =  2                              :            45818
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46179
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870179
   j =  1                              :        399907645
   j =  2                              :            46173
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.69
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.85
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.51
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.92
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.21
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.92
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.41
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.40
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.76
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.64
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17281.85
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.92
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.90
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.29
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.39
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.33
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.44
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.73
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.96
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.09
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.75
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.75
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.28
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.67
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.97
 p-value of test no 160                :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.64
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.41
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.12
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.37
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.43
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.22
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.15
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.04
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.65
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.60
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.74
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.50
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.62
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.14
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   30.72
 p-value of test no 176                :  2.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.96
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.78
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.38
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.21
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.89
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.96
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.93
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.84
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.63
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3923.14
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.36
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.20
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.91
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.12
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999995714
 
 Normal statistic for number of bits   :  -0.034
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.81
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000032287
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:34.44
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200867863.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27452
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.52
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.58
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.00
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.07
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.14
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.11
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.78
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.10
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.54
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.89
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.18
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.27
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.85
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.54
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908280
   j =  2                              :            45851
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908741
   j =  2                              :            45628
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
 p-value of test no 77                 :    0.9919
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.73
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.72
 p-value of test no 120                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.66
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.02
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.86
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.13
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.03
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.00
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17350.37
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.43
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.25
 p-value of test no 147                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.21
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.90
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.53
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.22
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.72
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.67
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.48
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.24
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.13
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.44
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.16
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.21
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.70
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.10
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.10
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.03
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.00
 p-value of test no 171                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.35
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.96
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.50
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.47
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.64
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.08
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.47
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.02
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.11
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9766.23
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.62
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.07
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.82
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.66
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.65
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.71
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.72
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000041818
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.71
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999922061
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.73
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201785367.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27453
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9938
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    4.23
 p-value of test no 32                 :  6.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.85
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.86
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.83
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.50
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.33
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.12
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  367.87
 p-value of test no 55                 :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.09
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.67
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.05
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.26
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.77
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.62
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908706
   j =  2                              :            45641
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907769
   j =  2                              :            46111
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.95
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.05
 p-value of test no 120                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.75
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.64
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.51
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.68
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.94
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.23
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.59
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.33
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17314.42
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.33
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.29
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.37
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.67
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.19
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.38
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.97
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.72
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.53
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.34
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.46
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.56
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.04
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.58
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.48
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.88
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.17
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.99
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.61
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.59
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.18
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.78
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.65
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.25
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.22
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.61
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.72
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.39
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.97
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.91
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.15
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.06
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.41
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.32
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.82
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.59
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.55
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.14
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.73
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000048481
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.67
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999941747
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
 p-value of test no 240                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:25.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202833943.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27454
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1498
 p-value of test no 11                 :  1.9e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334618
   j =  1                              :        599997004
   j =  2                              :             1498
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.96
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.65
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.41
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.79
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.33
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.13
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.47
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.58
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.58
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.63
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.23
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.98
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.80
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908721
   j =  2                              :            45635
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908287
   j =  2                              :            45852
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 103                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    5.43
 p-value of test no 105                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.58
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.08
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.53
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.41
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.50
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.56
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.05
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.05
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.85
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.84
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.23
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.72
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.66
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.04
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.80
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.09
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.98
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.61
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.16
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.56
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.07
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.33
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.03
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.21
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.61
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.73
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.48
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.51
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.18
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.59
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.33
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.94
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.72
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.83
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.15
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.30
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.92
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.64
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.87
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.26
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.27
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 188                :    0.98
 
 Sample variance                       :    2.42
 p-value of test no 189                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.82
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.21
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.40
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.55
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4727.49
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.82
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3930.18
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.38
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.97
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.21
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.74
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999932612
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.93
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000000829
 
 Normal statistic for number of bits   : 6.55e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    2.12
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:57.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203816983.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27455
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.10
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.52
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.28
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.20
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.76
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.84
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.79
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.21
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.51
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.92
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-4
 p-value of test no 62                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    5.33
 p-value of test no 64                 :  2.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  103.31
 p-value of test no 65                 :  4.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.21
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.76
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.27
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908167
   j =  2                              :            45912
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908513
   j =  2                              :            45742
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.08
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.43
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.74
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.13
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.05
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.90
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.63
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.36
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.59
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.55
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.05
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.71
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.57
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.92
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.60
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.83
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.28
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.99
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.43
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.55
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.27
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.01
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.70
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.42
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.86
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.67
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.54
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.08
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.72
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.78
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.96
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.04
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.88
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.81
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.00
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.08
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.86
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.93
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.14
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.03
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.09
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.26
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.24
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.20
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.09
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5053.74
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.57
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4394.69
 p-value of test no 228                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.64
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.42
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.54
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999976799
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.30
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000050398
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:31.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     4.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204865559.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27456
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.01
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.38
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.99
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.57
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.23
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.90
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.96
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.22
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.41
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908418
   j =  2                              :            45782
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907871
   j =  2                              :            46060
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.57
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.74
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.98
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.44
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.28
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.45
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.77
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.64
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.87
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.37
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.54
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.73
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.05
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.15
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.28
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.96
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.49
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.35
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.31
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.10
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.18
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.71
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.22
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.99
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.55
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.82
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.65
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.21
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.61
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.97
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.03
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.85
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.42
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.84
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.57
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.19
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.02
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.53
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.26
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.16
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.36
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.56
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-3
 p-value of test no 224                :    0.9989
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4658.29
 p-value of test no 226                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.15
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.56
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.89
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.55
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.69
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999909227
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.82
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999920102
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    2.17
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:19.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206012439.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27457
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7130
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4495
 p-value of test no 16                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.54
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.66
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   39.10
 p-value of test no 48                 :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.47
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.85
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.21
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.85
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.47
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.25
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.75
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.21
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.06
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.64
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.77
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.67
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45559
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869559
   j =  1                              :        399908883
   j =  2                              :            45557
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45564
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869564
   j =  1                              :        399908877
   j =  2                              :            45554
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  131.65
 p-value of test no 119                :  4.1e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.40
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.97
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.82
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.60
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.66
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.33
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.96
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17029.77
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.59
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.74
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.89
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.30
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.64
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.15
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.73
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.92
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.21
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.96
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.00
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.85
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.13
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.22
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.70
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.67
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.67
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.81
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.33
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.85
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.61
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.67
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.63
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.87
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.74
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.45
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.13
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.92
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.89
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.01
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.77
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.29
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.24
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.56
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.13
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.96
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.00
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.35
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.04
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000018415
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.31
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999867800
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 240                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 242                :  9.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:44.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            4.1e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207061015.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27458
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5309
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.70
 p-value of test no 41                 :  4.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.74
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.30
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.24
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.46
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.53
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.18
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.35
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.64
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.50
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.00
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.83
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.44
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.43
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908584
   j =  2                              :            45702
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908533
   j =  2                              :            45729
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.78
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.65
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.31
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.12
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.57
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.46
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.26
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.01
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.87
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.95
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.39
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.65
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.65
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.40
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.35
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.72
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.07
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.54
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.20
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.76
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.07
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.81
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.26
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.07
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.04
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.32
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.58
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.97
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.85
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.65
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.46
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.42
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.59
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.20
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.09
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.08
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.48
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.86
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.25
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.27
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.63
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.66
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.98
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.80
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.20
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3927.97
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.04
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12146.35
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11542.55
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.85
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999944765
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.38
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000106729
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.012
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:40.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208207895.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27459
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.23
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.98
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.39
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.27
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.05
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.84
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.87
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6836.51
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.53
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.69
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.10
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.11
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907958
   j =  2                              :            46018
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.04
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.76
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.69
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.60
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.24
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.57
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.80
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.80
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.42
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17756.79
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.29
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.67
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.79
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.22
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.80
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.96
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.96
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.97
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.58
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.31
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.63
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.45
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.95
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.46
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.75
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.65
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.12
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.38
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.26
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.97
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.94
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.40
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.04
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.13
 p-value of test no 172                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.46
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.46
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.72
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.33
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.57
 p-value of test no 203                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.37
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.29
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.72
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.46
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.69
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.21
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.03
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.02
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11523.76
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.97
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999918887
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.38
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999990554
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.53
 p-value of test no 248                :  5.8e-3
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
 p-value of test no 250                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.56
 p-value of test no 253                :  5.2e-3
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:54.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209256471.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27460
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 6                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 9                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     966
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.22
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.19
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.80
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.36
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.82
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.87
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.09
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  343.89
 p-value of test no 55                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.46
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7313.52
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.49
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.06
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.06
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.76
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.92
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907912
   j =  2                              :            46035
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45458
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869458
   j =  1                              :        399909088
   j =  2                              :            45450
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 103                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.49e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.87
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.85
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.45
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.27
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.54
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.56
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.69
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.58
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.92
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.18
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.25
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.31
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.32
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.58
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.12
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.18
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.42
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.98
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.49
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.82
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.25
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.70
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.47
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.47
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.94
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.91
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.18
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.60
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.23
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.51
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.55
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.53
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.09
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  462.29
 p-value of test no 169                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.88
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.59
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.55
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.09
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.36
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.94
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.33
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.99
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.13
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.76
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.71
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.74
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.90
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.41
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.55
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3970.75
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.58
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.21
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.92
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999974120
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.10
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000285919
 
 Normal statistic for number of bits   :    2.26
 p-value of test no 234                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.66e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:38.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   6  CollisionOver, t = 3            0.9990 
  35  Gap, r = 25                     0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188907521.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27461
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 11                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.47
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.63
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.26
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.35
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.40
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.77
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.77
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.75
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.59
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.79
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.08
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907899
   j =  2                              :            46046
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908039
   j =  2                              :            45976
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.98
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.77
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.23
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.83
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.99
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.40
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.70
 p-value of test no 125                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.73
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.13
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.090
 p-value of test no 135                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.08
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.57
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.28
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.24
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.66
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.84
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.17
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.83
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.62
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.23
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.91
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.26
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.22
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.77
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.50
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.02
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.04
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.84
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.31
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.85
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.02
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.30
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.92
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.11
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.65
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.58
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.41
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.85
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.00
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.21
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 204                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-3
 p-value of test no 205                :    0.9984
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 206                :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.35
 p-value of test no 207                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.64
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.82
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5072.72
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.71
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.30
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.62
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.59
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.27
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.83
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000033763
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.43
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000132625
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:18.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190644225.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27462
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 3                  :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.74
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.88
 p-value of test no 23                 :  3.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 29                 :    0.9969
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.70
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.89
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.52
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.82
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.64
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.99
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.62
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.59
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.38
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.73
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.03
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.52
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.71
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.41
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907987
   j =  2                              :            46002
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908240
   j =  2                              :            45871
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.22
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.25
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.84
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.38
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.14
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.24
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.98
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.88
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17567.50
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.71
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.43
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.96
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.77
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.34
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.83
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.79
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.73
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.20
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.16
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.41
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.91
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.77
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.71
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.57
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.14
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.28
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.88
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.10
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.26
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.03
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.80
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.49
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.96
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.89
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.49
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.67
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.77
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.42
 p-value of test no 177                :    0.9997    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.59
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.05
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.80
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.07
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.46
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.60
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.17
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.86
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.46
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.29
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.30
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.71
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000231922
 
 Normal statistic for number of bits   :    1.83
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.68
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999879173
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 245                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.43
 p-value of test no 248                :    0.9924
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:06.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191496193.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27463
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1238
 p-value of test no 10                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334358
   j =  1                              :        599997524
   j =  2                              :             1238
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 35                 :    0.9968
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.47
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.75
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.94
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.33
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.71
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.16
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.74
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.25
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.50
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.45
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.12
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.93
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907690
   j =  2                              :            46152
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46186
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907631
   j =  2                              :            46180
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
 p-value of test no 87                 :    0.9972
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.37
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.99
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.66
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.11
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.35
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.60
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.53
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.32
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.44
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
 p-value of test no 142                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 143                :  4.8e-4    *****
 
 Anderson-Darling statistic = A2       :    7.32
 p-value of test no 144                :  2.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18118.94
 p-value of test no 145                :  1.3e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.55
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.30
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.61
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.27
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.07
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.28
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.94
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.69
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.32
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.10
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.59
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.26
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.24
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.78
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.09
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.98
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.49
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.83
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.42
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.87
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.73
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.86
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.31
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.01
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.78
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.28
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  477.95
 p-value of test no 172                :  7.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.90
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.26
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.32
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.59
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.84
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.02
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.33
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.44
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.53
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.56
 p-value of test no 218                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.16
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.45
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.36
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.57
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12157.63
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.18
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.27
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999850688
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.39
 p-value of test no 233                :  5.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000071077
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:36.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9997 
  73  GCD                             1.3e-4
  79  RandomWalk1 M (L=10000, r=15)   7.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192446465.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27464
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 9                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.53
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    4.84
 p-value of test no 27                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    3.41
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.20
 p-value of test no 46                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.84
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.28
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.29
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.60
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  355.07
 p-value of test no 55                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.49
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.91
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.54
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.69
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.71
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.21
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.35
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907952
   j =  2                              :            46015
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.81
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.44
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.06
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.64
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.07
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.35
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.09
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.41
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.64
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.20
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.53
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.51
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.96
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.95
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.86
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.10
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.26
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.37
 p-value of test no 152                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.31
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.43
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.68
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.66
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.28
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.38
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.17
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.28
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.24
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.87
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.39
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.41
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.96
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.80
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.53
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.24
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.80
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.30
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.23
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.87
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.85
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.90
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.11
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.94
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.02
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.77
 p-value of test no 198                :  2.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.73
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 204                :  4.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    4.85
 p-value of test no 206                :  3.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.39
 p-value of test no 207                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
 p-value of test no 208                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10317.48
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.40
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.44
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.13
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4379.14
 p-value of test no 227                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.68
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.50
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.44
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.96
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000046510
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.23
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000053269
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 253                :  8.3e-3
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:46.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193888257.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27465
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5255
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.26
 p-value of test no 34                 :  8.0e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 39                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.03
 p-value of test no 46                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.89
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.11
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.68
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.84
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.46
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.12
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.71
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.70
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.21
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.99
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.65
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.17
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908480
   j =  2                              :            45751
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908360
   j =  2                              :            45811
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.47e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 114                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.01
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.44
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.37
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.97
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.09
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.49
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.69
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.59
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.56
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17292.90
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.64
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.35
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.66
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.82
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.93
 p-value of test no 151                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.33
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.95
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.76
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.40
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.54
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.77
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.46
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.59
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.56
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.95
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.64
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.61
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.73
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.80
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.46
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.30
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.85
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.90
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.44
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.48
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.78
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.02
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.81
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.70
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.99
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.04
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.76
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.15
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.85
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.03
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.09
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.54
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.87
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.76
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.45
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999898544
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.74
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999853724
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 243                :    0.98
 
 Sample variance                       :    2.11
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
 p-value of test no 250                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:20.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            8.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194838529.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27466
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1224
 p-value of test no 11                 : 1 -  6.0e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334344
   j =  1                              :        599997552
   j =  2                              :             1224
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 26                 :    0.9976
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.68
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.75
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.37
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.32
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.41
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.14
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.28
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.19
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.38
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.87
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.45
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.30
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.22
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908505
   j =  2                              :            45740
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908244
   j =  2                              :            45869
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  6.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.56
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.51
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.26
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.55
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.45
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.76
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.24
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.44
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.36
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.37
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.41
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.99
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.91
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.35
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.79
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.02
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.40
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.57
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.48
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.94
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.25
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.58
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.77
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.63
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.06
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.59
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.84
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.38
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.05
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.45
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.22
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.31
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.81
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.15
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.34
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.32
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.06
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.92
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.63
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.99
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.55
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.02
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.36
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.06
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.91
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.37
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.60
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.48
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.09
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000033121
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.95
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999988664
 
 Normal statistic for number of bits   :  -0.090
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.38e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:35.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  6.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195690497.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27467
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 23                 :    0.9973
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.20
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.25
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.38
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.20
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.21
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.73
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.77
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.21
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.92
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.82
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.76
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.32
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.03
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908441
   j =  2                              :            45775
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908488
   j =  2                              :            45750
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 87                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -3.29e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.46
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.47
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.24
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.63
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.53
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.08
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.09
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.80
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.18
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.09
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.83
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17232.90
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.53
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.34
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.82
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.60
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.20
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.90
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.00
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.52
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.23
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.71
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.38
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.19
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.24
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.87
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.46
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.54
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.84
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.50
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.90
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.89
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.07
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.38
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.33
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.36
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.25
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  144.39
 p-value of test no 175                :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.38
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.12
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.81
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.27
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.29
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.91
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.95
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.57
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.23
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.61
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.51
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.30
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999971498
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.21
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999951407
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.08
 
 Sample variance                       :    2.24
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:53.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196575233.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27468
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 10                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    3.38
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    2.94
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.36
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.60
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.38
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.99
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.11
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.12
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.27
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.95
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.74
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908261
   j =  2                              :            45859
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907843
   j =  2                              :            46071
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.36
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.97
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.43
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.29
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.78
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.08
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.29
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.31
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.62
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.00
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.74
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.12
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.34
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.53
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.37
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.10
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.40
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.40
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.91
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.94
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.04
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.16
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.74
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.46
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.92
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.45
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.87
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.07
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.17
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.81
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.04
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.07
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.06
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.40
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.22
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.40
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.85
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.57
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.70
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.66
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.93
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.16
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.86
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10277.75
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.36
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.24
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3914.08
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.43
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.55
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.42
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.88
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999997331
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.94
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000275848
 
 Normal statistic for number of bits   :    2.18
 p-value of test no 234                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:21.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197492737.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27469
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.11
 p-value of test no 28                 :  7.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.79
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.51
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.40
 p-value of test no 49                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.26
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.92
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.84
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.48
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.54
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.91
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.88
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.21
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.73
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.67
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.75
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.50
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907950
   j =  2                              :            46019
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907884
   j =  2                              :            46055
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.50
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.33
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.04
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.13
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.63
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.09
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.47
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.64
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.73
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17664.59
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.16
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.82
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.67
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.58
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.11
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.79
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.54
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.09
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.27
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.19
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.88
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.01
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.64
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.51
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.69
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.65
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.57
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.27
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.62
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.17
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.52
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.98
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.09
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.05
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.92
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.23
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.80
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.86
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.82
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :-2.81e-16
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.63
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.66
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 206                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  259.86
 p-value of test no 207                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.94
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.78
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.71
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.36
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.33
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.82
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.11
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.59
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.37
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999999560
 
 Normal statistic for number of bits   : -3.48e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.10
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000083200
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:46.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  29  SimpPoker, r = 25               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198639617.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27470
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 9                  :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5298
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.62
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.47
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.02
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.96
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.88
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.75
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.33
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.23
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.98
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7000.01
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.14
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.18
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.53
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.71
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.98
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907971
   j =  2                              :            46007
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908281
   j =  2                              :            45852
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-4
 p-value of test no 97                 :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 9.62e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.85
 p-value of test no 119                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.48
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.11
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.30
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.21
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.25
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.19
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.21
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.72
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.27
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.12
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.46
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.74
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.90
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.35
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.49
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.63
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.73
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.45
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.50
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.97
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.72
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.39
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.11
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.03
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.16
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.86
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.76
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.69
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.08
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.60
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.56
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.57
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.07
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.66
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.44
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.15
 p-value of test no 198                :    0.9972
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.03
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.80
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.44
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.74
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.32
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.09
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.41
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.19
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.22
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.94
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.18
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999997982
 
 Normal statistic for number of bits   :  -0.016
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.41
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000129307
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:35.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199852033.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27471
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    3.53
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.45
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.54
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.19
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.18
 p-value of test no 52                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.52
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.31
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.47
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6878.01
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.54
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.38
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.34
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.26
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46259
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870259
   j =  1                              :        399907483
   j =  2                              :            46257
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908486
   j =  2                              :            45754
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  4.8e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-4
 p-value of test no 100                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 108                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.055
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.50
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.93
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.23
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.47
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.62
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.26
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.06
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.34
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.77
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17417.62
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.32
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.54
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.17
 p-value of test no 148                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.41
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.92
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.46
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.15
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.21
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.06
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.69
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.68
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.20
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.70
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.92
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.77
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.36
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.46
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.32
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.29
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.72
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.73
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.09
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.97
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.81
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.25
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.80
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.05
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.74
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.97
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.78
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.12
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.80
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.60
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.28
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 213                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10315.34
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.87
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.19
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.51
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.58
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.31
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.77
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.50
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000091855
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.48
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999920723
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:19.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200835073.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27472
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5298
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    3.66
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.72
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.18
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.45
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.07
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.50
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.38
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.22
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.28
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.61
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.74
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.97
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.16
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.94
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907887
   j =  2                              :            46049
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908440
   j =  2                              :            45777
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.35
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.60
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.98
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.18
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.47
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.26
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.59
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.45
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.74
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.79
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.28
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.78
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.48
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.66
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.88
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.18
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.88
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.40
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.64
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.61
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.46
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.01
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.49
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.44
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.72
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.12
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.62
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.00
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.46
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.63
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.27
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.44
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.47
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.53
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    2.37
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 186                :  9.8e-5    *****
 
 Anderson-Darling statistic = A2       :    5.59
 p-value of test no 187                :  1.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.67
 p-value of test no 188                :  3.8e-3
 
 Sample variance                       :    0.14
 p-value of test no 189                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.32
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.97
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.62
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.79
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.93
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.39
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.68
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.01
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.57
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.37
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.82
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.11
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.04
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000043012
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.33
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000070585
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 238                :    0.9911
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:25.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201949185.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27473
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.82
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.13
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.29
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.90
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.23
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.42
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.81
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.60
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.72
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.17
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.87
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.20
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4902.33
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908222
   j =  2                              :            45886
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908376
   j =  2                              :            45809
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
 p-value of test no 97                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.44
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.29
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.03
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.46
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.72
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.23
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.66
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.14
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.37
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.96
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.09
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.85
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.67
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.78
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.82
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.47
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.60
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.24
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.07
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.23
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.26
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.77
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.89
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.69
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.56
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.01
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.69
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.08
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.16
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.72
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.25
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.29
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.78
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.60
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.79
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.11
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.99
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.98
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.67
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.03
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.84
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    2.05
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 190                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 192                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.35
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.57
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.72
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.36
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.21
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.32
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.92
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.01
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.82
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.06
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.79
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.82
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000174772
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.66
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000040375
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:20.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202964993.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27474
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     114
 p-value of test no 43                 :    0.9987
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.21
 p-value of test no 48                 :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.83
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.45
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.52
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.09
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.58
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.09
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1287.70
 p-value of test no 56                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.38
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.41
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.53
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.21
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.37
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4948.12
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908062
   j =  2                              :            45957
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908119
   j =  2                              :            45936
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.74
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.51
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.71
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.38
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.86
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.40
 p-value of test no 124                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.86
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.09
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.98
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.92
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.22
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17229.01
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.79
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.47
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.60
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.98
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.63
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.34
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.23
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.32
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   99.56
 p-value of test no 156                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.44
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.26
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.27
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.76
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.71
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.63
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.40
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.08
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.97
 p-value of test no 165                :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.38
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.37
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.07
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.93
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.65
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.06
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.85
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.89
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.45
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.77
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.22
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.84
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.21
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.24
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.96
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10221.13
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.66
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.93
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.61
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.04
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.84
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.55
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.70
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999864410
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.33
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000182611
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    3.00
 p-value of test no 249                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:54.48
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204111873.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27475
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.24
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.29
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.87
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.82
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.57
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.67
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.48
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.97
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.72
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.72
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.10
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.54
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.20
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.84
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.10
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.45
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908882
   j =  2                              :            45556
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908383
   j =  2                              :            45807
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.87
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.67
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.83
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.86
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.34
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.03
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.05
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17525.14
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.37
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.07
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.86
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.11
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.50
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.77
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.52
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.66
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.16
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.18
 p-value of test no 156                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.65
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.54
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.80
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.10
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.36
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.27
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.84
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.40
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.25
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.99
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.19
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.19
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.69
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.80
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.36
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5272.48
 p-value of test no 173                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.80
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.02
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.03
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.80
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.02
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.32
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.72
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.07
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.50
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.99
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.43
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.01
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11553.23
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.30
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.29
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999968957
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.72
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999982601
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :   0.094
 p-value of test no 244                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:15.72
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205160449.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27476
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.93
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.74
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.14
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.89
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.27
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.62
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.40
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1332.38
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.19
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.61
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.94
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.15
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.19
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5193.89
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908362
   j =  2                              :            45810
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908526
   j =  2                              :            45725
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.50
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.30
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.15
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.63
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.27
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.20
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.40
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.35
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 144                :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.37
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.69
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.08
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.51
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.01
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.08
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.24
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.48
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.83
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.31
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.65
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.03
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.60
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.90
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.11
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.86
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.72
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.00
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.45
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.32
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.24
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.30
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.19
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.34
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.26
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.96
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.73
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.33
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
 p-value of test no 200                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.34
 p-value of test no 203                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 206                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.39
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.61
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.76
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.96
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.98
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.48
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.93
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.97
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.97
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.23
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000017878
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.27
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999979079
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
 p-value of test no 245                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:08.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206241793.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27477
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7112
 p-value of test no 19                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    2.95
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.13
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.75
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.02
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.97
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.10
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.68
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.20
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.71
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.08
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.95
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.11
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.32
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.59
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.44
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.54
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908466
   j =  2                              :            45764
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908158
   j =  2                              :            45915
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.71
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  104.48
 p-value of test no 120                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.20
 p-value of test no 121                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.28
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.91
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.08
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.87
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.45
 p-value of test no 134                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.75
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17049.96
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.11
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.86
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.23
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.81
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.36
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.34
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.47
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.71
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.79
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.45
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.13
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.89
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.29
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.43
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.40
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.20
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.96
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.46
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.50
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.17
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.79
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.75
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.95
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.04
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5202.67
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.39
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.69
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.47
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.55
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.60
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.80
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.67
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.23e-4
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.92
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.47
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.50
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.04
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11531.95
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.44
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.67
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000154837
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.94
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999864608
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:51.98
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207192065.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27478
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.35
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.43
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.14
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.75
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   25.76
 p-value of test no 51                 :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.25
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.24
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.72
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.01
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.50
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.46
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.95
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.86
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.43
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907904
   j =  2                              :            46036
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908313
   j =  2                              :            45839
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
 p-value of test no 109                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.82
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.45
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.91
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.05
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.16
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.46
 p-value of test no 124                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.12
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.38
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.16
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.12
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17609.13
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.31
 p-value of test no 146                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.14
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.99
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.48
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.88
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.04
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.32
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.63
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.08
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.37
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.16
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.35
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.59
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.73
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.89
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.22
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.86
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.63
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.05
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.61
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.64
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.72
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.38
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.77
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.39
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.81
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.03
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.99
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.98
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.78
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.68
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.67
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.01
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.40
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.94
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.16
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.75
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.52
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.41
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.56
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999989582
 
 Normal statistic for number of bits   :  -0.082
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.73
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999843314
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.012
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-3
 p-value of test no 251                :    0.9989
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 253                :    0.9915
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:31.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208306177.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27479
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7540
 p-value of test no 20                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.85
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     531
 p-value of test no 31                 :    0.9978
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    4.79
 p-value of test no 39                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.40
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.15
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.55
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.57
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.27
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1547.67
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7175.95
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.54
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.15
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.34
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.03
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908605
   j =  2                              :            45693
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908290
   j =  2                              :            45852
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.19
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.00
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.97
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.73
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.76
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.35
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.71
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.50
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.25
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.33
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.21
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.18
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.51
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.20
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.00
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.61
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.79
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.81
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.58
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.79
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.82
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.07
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.04
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.23
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.92
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.03
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.49
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.41
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.83
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.89
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.35
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.27
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.83
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.88
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.20
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.66
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.27
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.24
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.57
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.47
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.42
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.31
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.83
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.18
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.66
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.72
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.18
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.59
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.11
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.17
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.37
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.13
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999995813
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.72
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000023236
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:37.90
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209354753.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27480
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.50
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.73
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.70
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.62
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   86.19
 p-value of test no 52                 :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.04
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.36
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.79
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.00
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.72
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.44
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.88
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.37
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.43
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907752
   j =  2                              :            46112
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908430
   j =  2                              :            45779
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 80                 :  5.2e-5    *****
 
 Anderson-Darling statistic = A2       :    9.51
 p-value of test no 81                 :  2.4e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  5.0e-5    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-4
 p-value of test no 98                 :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.31
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.18
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.70
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.54
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.16
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.46
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.80
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.50
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 130                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.14
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.38
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.46
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.84
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.66
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.54
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.57
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.87
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.75
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.56
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.08
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.35
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.73
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.80
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.42
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.68
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.09
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.38
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.90
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.63
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.96
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.26
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.39
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.19
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.81
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.77
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.69
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.90
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.70
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.64
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.20
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.56
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.27
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.24
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.10
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.56
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.10
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.72
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.65
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.74
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.78
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.45
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.91
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.08
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.37
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000107695
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.68
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000011488
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:36.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  5.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188940290.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27481
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.05
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.80
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.54
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.26
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.57
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.74
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.03
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.65
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.58
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.23
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.51
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.55
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.05
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.80
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5201.88
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907808
   j =  2                              :            46093
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45633
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869633
   j =  1                              :        399908736
   j =  2                              :            45629
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.08
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.89
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.04
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.43
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.98
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.32
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.61
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.79
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.47
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.96
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.78
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17843.65
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.98
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.77
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.75
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.01
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.02
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.52
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.03
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.00
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.09
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.47
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.09
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.16
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.91
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.76
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.08
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.87
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.97
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.82
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.37
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.78
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.73
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.40
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.96
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.96
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.00
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.63
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.74
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.29
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.94
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.28
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.28
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.43
 p-value of test no 217                :  3.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.14
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.34
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3900.90
 p-value of test no 227                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.46
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12127.09
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.08
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.02
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000079105
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.33
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999998132
 
 Normal statistic for number of bits   :  -0.015
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    2.50
 p-value of test no 254                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:20.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300            3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190218242.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27482
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997189
   j =  2                              :             1404
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.64
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.56
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.42
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.48
 p-value of test no 51                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.54
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.28
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.18
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1316.85
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7195.71
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.30
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.65
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.08
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.58
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.47
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908331
   j =  2                              :            45830
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45667
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869667
   j =  1                              :        399908668
   j =  2                              :            45663
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.57
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.34
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.19
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.53
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.53
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.36
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.62
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.24
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.23
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17669.73
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.28
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.51
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.49
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.25
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.95
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.89
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.24
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.91
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.67
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.23
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.96
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.91
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.96
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.64
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.04
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.15
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.82
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.11
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.23
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.17
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.06
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.55
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.49
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.62
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.43
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.09
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.09
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.10
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.86
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.76
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.0e-3
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10358.22
 p-value of test no 215                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.77e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.69
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.45
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.75
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.83
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.82
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.18
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.36
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000083506
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.46
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000070690
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:21.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191397890.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27483
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    3.52
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     185
 p-value of test no 43                 :  3.2e-3
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.02
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.41
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.31
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.90
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.96
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.78
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.05
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.89
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1543.72
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.67
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.88
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.71
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.55
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.53
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907930
   j =  2                              :            46029
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907891
   j =  2                              :            46053
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 85                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.30
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.40
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.82
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.41
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.74
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.23
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.43
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.62
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.35
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.39
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   98.86
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17743.19
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.87
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.45
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.14
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.07
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.79
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.03
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.55
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.65
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.59
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.50
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.09
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.42
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.15
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.29
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.24
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.41
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.94
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.79
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.69
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.34
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.85
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.24
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.50
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.61
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.83
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.78
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.04
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.43
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.25
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.18
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.43
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.71
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.17
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.52
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.21
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.05
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.81
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3951.23
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.49
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.78
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.37
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.53
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999975371
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.79
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000134539
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    2.16
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:59.85
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192380930.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27484
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 7                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 9                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 12                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5553
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.75
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.05
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.96
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.06
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.20
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.34
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.94
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.49
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.19
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.99
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.08
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.16
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.12
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.30
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.56
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.66
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45571
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869571
   j =  1                              :        399908862
   j =  2                              :            45563
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46335
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870335
   j =  1                              :        399907334
   j =  2                              :            46327
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
 p-value of test no 84                 :    0.9963
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.77
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.99
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.51
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.96
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.20
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17536.45
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.95
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.99
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.97
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.48
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.30
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.09
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.53
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.47
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.56
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.59
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.39
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.75
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.67
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.78
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.49
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.19
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.44
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.51
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.20
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.77
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.77
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.13
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.05
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.00
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.35
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.45
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.43
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.02
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.58
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.20
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.49
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.78
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.70
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.43
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.26
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.27
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999994133
 
 Normal statistic for number of bits   :  -0.046
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.73
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999876782
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:38.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193265666.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27485
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.69
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.81
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.60
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.90
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.76
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.21
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.06
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.52
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.84
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.07
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.93
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.06
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.69
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908047
   j =  2                              :            45969
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45439
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869439
   j =  1                              :        399909128
   j =  2                              :            45427
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-4
 p-value of test no 109                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-6
 p-value of test no 110                :    0.9970
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.06
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.55
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.54
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.84
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.48
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.39
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.58
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.85
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.84
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17269.37
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.34
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.17
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.99
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.14
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.60
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.90
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.90
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.22
 p-value of test no 157                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.77
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.07
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.06
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.01
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.76
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.84
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.69
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.33
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.22
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.63
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.39
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.76
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.36
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.71
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.21
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.38
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.05
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.36
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.57
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.15
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.33
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.87
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.33
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.42
 p-value of test no 216                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.25
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.84
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.70
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.74
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.70
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12201.55
 p-value of test no 230                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.51
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000017440
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.00
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999879980
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 246                :    0.9953
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:46.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194281474.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27486
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7122
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.80
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.46
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.73
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.68
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.07
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.76
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.07
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.43
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.38
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.46
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.01
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.00
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.64
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.11
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908335
   j =  2                              :            45831
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908183
   j =  2                              :            45904
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.88
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.35
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.56
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.56
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.35
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.00
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.59
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.07
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.19
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.79
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17124.91
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.41
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.78
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.05
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.28
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.71
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.87
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.95
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.44
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.26
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   91.03
 p-value of test no 159                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.54
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.07
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.26
 p-value of test no 163                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.35
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.70
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.64
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.72
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.50
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.99
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.36
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.49
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.63
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.46
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.18
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.43
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.58
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.95
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.43
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.64
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.30
 p-value of test no 207                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 209                :  1.2e-3
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 210                :  4.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10340.34
 p-value of test no 211                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.68
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.49
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.52
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.15
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.44
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.98
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.47
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.69
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000041557
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.22
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999993479
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:45.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195231746.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27487
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.98
 p-value of test no 45                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.87
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.91
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.83
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.08
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.42
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.11
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.17
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.44
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1536.30
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.90
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.07
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.83
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.61
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.73
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.23
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907902
   j =  2                              :            46043
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908231
   j =  2                              :            45874
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
 p-value of test no 72                 :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  7.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -3.81e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.84
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.23
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.38
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.32
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.22
 p-value of test no 123                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.31
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.19
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.26
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.99
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.06
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.19
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  174.07
 p-value of test no 141                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.46
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.77
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.50
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.62
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.08
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.72
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.23
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.03
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.69
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.32
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.84
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.36
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.08
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.64
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.85
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.14
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.74
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.75
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.53
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.57
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.99
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.56
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.93
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.12
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.63
 p-value of test no 170                :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.44
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.49
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.15
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.07
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.81
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.93
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.51
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.50
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.96
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.91
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.33
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.63
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4696.12
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.13
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.25
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.78
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.26
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.09
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999985103
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.01
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000127306
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:20.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196345858.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27488
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 4                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.69
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.83
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.67
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.20
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.25
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.17
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.22
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.85
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.71
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.42
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.00
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.34
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.29
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.69
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.49
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5221.68
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907760
   j =  2                              :            46117
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.07e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.45
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.65
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.05
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.42
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.47
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.46
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.23
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.25
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.43
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.57
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.14
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.22
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.41
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.94
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.82
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.33
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.13
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.34
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.94
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.82
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.81
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.02
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.56
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.70
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.73
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.65
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.90
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.76
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.03
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.52
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.23
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.35
 p-value of test no 172                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.58
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.28
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.08
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.35
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.91
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.21
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.32
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.53
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.37
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.12
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.59
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.13
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.98
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.02
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.07
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.68
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.45
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999962768
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   95.58
 p-value of test no 233                :  4.2e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000070069
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
 p-value of test no 241                :    0.9967
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:48.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             4.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197296130.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27489
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.79
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.18
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.65
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.90
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.77
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.83
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.58
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.29
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.95
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.62
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.22
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.22
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.78
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.94
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.70
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907996
   j =  2                              :            46002
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.45
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.34
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.58
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.20
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.90
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.11
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.71
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.53
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17667.64
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.63
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.62
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.83
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.26
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.55
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.44
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.83
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.60
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.51
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.29
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.85
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.84
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.69
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.37
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.40
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.95
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.71
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.19
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.23
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.65
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.49
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.74
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.46
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.30
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.00
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.82
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.03
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.32
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.76
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.05
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.51
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.50
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.25
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.33
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.20
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.50
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 224                :    0.9957
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4656.31
 p-value of test no 226                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.17
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.24
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.06
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.42
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.82
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999913046
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.42
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000121630
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:09.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198344706.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27490
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 8                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     256
 p-value of test no 37                 :    0.9949
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.25
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.59
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.58
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.47
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.10
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.36
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.18
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.48
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.74
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.95
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.02
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.38
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5207.36
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907886
   j =  2                              :            46051
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908108
   j =  2                              :            45937
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.34
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.10
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.20
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.41
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.28
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.89
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.37
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.20
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.84
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.87
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.12
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17602.80
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.92
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.99
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.10
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.24
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.48
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.59
 p-value of test no 152                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.54
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.76
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.03
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.72
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.25
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.58
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.25
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.16
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.55
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.11
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.78
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.68
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.59
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.00
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.20
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.10
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.17
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.50
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.38
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.87
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.86
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.61
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.37
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.32
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.21
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.17
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.52
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.92
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.59
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.85
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.65
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.39
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.54
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999999923
 
 Normal statistic for number of bits   : -6.09e-4
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.31
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000116242
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.048
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:43.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199491586.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27491
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 9                  :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.14
 p-value of test no 29                 :    0.9992    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9948
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    4.27
 p-value of test no 42                 :  6.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.97
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.40
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.30
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.43
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.19
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.13
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.06
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1548.08
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.76
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.76
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.53
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.77
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.76
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4846.84
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908194
   j =  2                              :            45897
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.30
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.92
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.95
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.01
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.36
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.83
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.00
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.41
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.49
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.54
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.84
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.10
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.59
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.72
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.23
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.40
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.10
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.88
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.88
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.24
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.25
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.82
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.98
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.60
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.63
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.22
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.49
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.97
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.19
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.48
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.64
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.73
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.17
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.95
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.63
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.46
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.88
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.09
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.67
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.47
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.42
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.22
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.67
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.62
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.14
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.63
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.71
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.18
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.59
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.59
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999946655
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.24
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999903956
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    2.39
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:01.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP, t = 5           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200638466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27492
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997203
   j =  2                              :             1397
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1231
 p-value of test no 11                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334351
   j =  1                              :        599997538
   j =  2                              :             1231
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 12                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5565
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7135
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.84
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.81
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.76
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  298.99
 p-value of test no 54                 :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  499.51
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.21
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.60
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.74
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.01
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.32
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.58
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.54
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45433
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869433
   j =  1                              :        399909140
   j =  2                              :            45421
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907730
   j =  2                              :            46129
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.66
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.31
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.98
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.61
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.57
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.54
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.45
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.95
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.44
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17106.74
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.05
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.47
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.82
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.19
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.55
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.55
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.23
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.44
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.46
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.32
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.60
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.07
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.38
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.17
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.69
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.17
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.53
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.92
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.58
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.19
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.93
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.69
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.99
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.10
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.34
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.52
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.99
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.26
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.69
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.38
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.97
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.03
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.68
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.70
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.70
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.62
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.15
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.43
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.63
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.45
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.27
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999912275
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.12
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000082417
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.068
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:35.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201654274.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27493
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.73
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.17
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.22
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.78
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.71
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.22
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.74
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.06
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1590.20
 p-value of test no 56                 :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6842.58
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.14
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.51
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.26
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.01
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.92
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908505
   j =  2                              :            45743
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908083
   j =  2                              :            45957
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.47
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.67
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.40
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.93
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.00
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.93
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.65
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.82
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.08
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17598.44
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.27
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.82
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.20
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.22
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.56
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.96
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.64
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.22
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.28
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.55
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.81
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.08
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.44
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.87
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.40
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.85
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.77
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.85
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.74
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.14
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.64
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.89
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.06
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.87
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.09
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.32
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.56
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.69
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.52
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.85
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.99
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.14
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.24
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.55
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.76
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.20
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.76
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12193.20
 p-value of test no 230                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.64
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000068011
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.73
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000003016
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:17.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202702850.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27494
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 11                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    3.08
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.27
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.70
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.00
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.29
 p-value of test no 50                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.37
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.95
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.22
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.18
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.88
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.36
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.42
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.90
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.94
 p-value of test no 66                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.69
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.12
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908252
   j =  2                              :            45874
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908345
   j =  2                              :            45826
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 118                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.56
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.95
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.79
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.85
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.68
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.03
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.68
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 135                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.03
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17459.93
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.03
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.70
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.27
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.45
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.51
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.28
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.73
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.99
 p-value of test no 154                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.11
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.86
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.11
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.85
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  181.37
 p-value of test no 159                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.66
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.67
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.29
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.12
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.93
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.99
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.09
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.07
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.39
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.40
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.97
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.59
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.05
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.04
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.38
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.46
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.42
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    2.37
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.03
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.23
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.23
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.10
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.56
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10313.49
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.30
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.25
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.96
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4268.95
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.64
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.23
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.63
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000091999
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.43
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999998591
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:12.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203784194.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27495
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1486
 p-value of test no 7                  :  6.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334606
   j =  1                              :        599997028
   j =  2                              :             1486
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.70
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.86
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.94
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.33
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.98
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.37
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7313.27
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.35
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.87
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.73
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.45
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.85
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908364
   j =  2                              :            45812
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908213
   j =  2                              :            45892
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-4
 p-value of test no 110                :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.32
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.60
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.06
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.91
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.76
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.22
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.88
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.02
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.13
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.52
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.56
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.87
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.82
 p-value of test no 148                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.74
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.95
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.47
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.94
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.24
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.06
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.31
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.45
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.97
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.54
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.24
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.35
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.39
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.63
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.36
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.12
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.62
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.67
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.90
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.87
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.49
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.29
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.46
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.55
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.61
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.73
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.69
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    2.52
 p-value of test no 184                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.30
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.78
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.45
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.43
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.31
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.72
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.44
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.17
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.86
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12090.82
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.61
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.24
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999837206
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.23
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000041713
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:15.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            6.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204767234.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27496
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.37
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.30
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.25
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.50
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.43
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.55
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  176.46
 p-value of test no 54                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.59
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.42
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7338.17
 p-value of test no 57                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 59                 :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.10
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.94
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.79
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.73
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908107
   j =  2                              :            45939
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908328
   j =  2                              :            45833
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.09
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.80
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.17
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.44
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.22
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.31
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 128                :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.66
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.14
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.45
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.00
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.25
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.83
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.62
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.99
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.63
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.12
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.44
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.88
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.06
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.12
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.86
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.07
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.56
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.67
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.94
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.34
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.64
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.85
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.27
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.22
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.72
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.71
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.22
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.81
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.48
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.00
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.27
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.63
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.37
 p-value of test no 176                :    0.9923
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.65
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.90
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.45
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.83
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.15
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.57
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.07
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3955.76
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.86
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.18
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.24
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.83
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000108832
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.76
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000044377
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:17.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205815810.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27497
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.72
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.16
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.04
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.56
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.79
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.79
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.52
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.70
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.45
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.25
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.39
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908343
   j =  2                              :            45827
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908195
   j =  2                              :            45901
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.91
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.84
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.34
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.12
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.61
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.01
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.94
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.07
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.26
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.33
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.44
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.89
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.43
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.16
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.83
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.91
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.97
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.90
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.22
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.51
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.57
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.28
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.09
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.59
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.73
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.06
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.75
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.74
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.66
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.45
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.55
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.61
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.35
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.80
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.31
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.22
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.11
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.58
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.91
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.00
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.64
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.51
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.20
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.96
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4676.09
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.24
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.22
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.82
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.40
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.62
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000040612
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.21
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000072814
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
 p-value of test no 246                :    0.9960
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.64
 p-value of test no 248                :    0.9959
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:57.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206798850.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27498
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 12                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.02
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.20
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.18
 p-value of test no 50                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.75
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.56
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.77
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.45
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.80
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.77
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.74
 p-value of test no 59                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.49
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.94
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.76
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  158.98
 p-value of test no 67                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.48
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908303
   j =  2                              :            45841
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908010
   j =  2                              :            45992
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.44
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.50
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.85
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.01
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.44
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.69
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.45
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.26
 p-value of test no 134                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.73
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.77
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 142                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17757.50
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.62
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.97
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.42
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.84
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.97
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.07
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.75
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.17
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.42
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.74
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.40
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.01
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.94
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.21
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.46
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.66
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.47
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.28
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.72
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.17
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.85
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.90
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.90
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.14
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.83
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.02
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.06
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.13
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.36
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.51
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.69
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.67
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.94
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.20
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.39
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.59
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.04
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.59
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.20
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.79
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000149773
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.11
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999657419
 
 Normal statistic for number of bits   :   -2.71
 p-value of test no 234                :    0.9966
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 240                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 247                :    0.9983
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:53.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207978498.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27499
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 8                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     837
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.17
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.69
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.93
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.16
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.97
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.89
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.74
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.92
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6869.14
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.97
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.12
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.59
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.38
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.06
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908192
   j =  2                              :            45901
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907816
   j =  2                              :            46086
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.77
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.16
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.78
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.85
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.16
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.35
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.01
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.03
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.39
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17153.01
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.54
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.40
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.30
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.78
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.60
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.15
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.18
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.82
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.69
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.83
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.73
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.09
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.54
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.85
 p-value of test no 161                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.44
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  191.82
 p-value of test no 164                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.10
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.94
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.74
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4773.49
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.92
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.76
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.79
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.90
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.48
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.94
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.33
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.55
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.65
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.22
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.58
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.86
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.76
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.87
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.71
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.04
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.86
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.52
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.53
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.44
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000000151
 
 Normal statistic for number of bits   : 1.19e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.32
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000121489
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 240                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:57.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208994306.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27500
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 11                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7515
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.91
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.99
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.95
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.92
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.77
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.35
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.74
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.52
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.97
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.77
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.87
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.04
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.91
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.28
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908436
   j =  2                              :            45779
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908516
   j =  2                              :            45739
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
 p-value of test no 106                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.17
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.20
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.13
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.64
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.61
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.69
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.28
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.67
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.44
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.45
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.01
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.96
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.99
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.73
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.78
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.44
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.72
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.85
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.45
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.60
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.82
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.10
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.34
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.60
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.68
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.69
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.40
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.29
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.89
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.00
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.55
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.56
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.72
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.12
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.54
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.68
 p-value of test no 171                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.20
 p-value of test no 172                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.56
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.24
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.60
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.71
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 185                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-4
 p-value of test no 191                :    0.9970
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.24
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.55
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.82
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.40
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.81
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.49
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.04
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.98
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.08
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.42
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.51
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.36
 p-value of test no 231                :  4.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999997037
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.09
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999969566
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:56.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 188973059.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27501
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7117
 p-value of test no 18                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.23
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.20
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.82
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.46
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.24
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.08
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.54
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.86
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.20
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6792.08
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.02
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.94
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.98
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.61
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908168
   j =  2                              :            45907
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908695
   j =  2                              :            45648
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  7.6e-3
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.31
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.96
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.49
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.81
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.63
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.16
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.44
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.53
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.61
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.58
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.32
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.56
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.26
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.30
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.34
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.51
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.72
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.29
 p-value of test no 159                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.30
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.45
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.36
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.08
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.43
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.15
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.43
 p-value of test no 167                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4767.24
 p-value of test no 168                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.46
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.21
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.48
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.44
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.03
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.61
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.76
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.65
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.29
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.91
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.09
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.92
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.23
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.10
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.49
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.41
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.90
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.12
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.34
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.93
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999911648
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.04
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999986486
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:55.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190382083.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27502
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.34
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.68
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.07
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.39
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.19
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.37
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.60
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.11
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.25
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 64                 :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.33
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.16
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5273.75
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908362
   j =  2                              :            45816
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907878
   j =  2                              :            46055
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.95
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.31
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.67
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.21
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.55
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.29
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.33
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.36
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17615.85
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.05
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.79
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.12
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.71
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.28
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.03
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.06
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.81
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.50
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.69
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.35
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.60
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.91
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.17
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.29
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.13
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.52
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.07
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.75
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.38
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.98
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.76
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.04
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.54
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.27
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.52
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.07
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.23
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.38
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.49
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.24
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.52
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3909.53
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.90
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.05
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.40
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999963359
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.87
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000058867
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 235                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.99
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:51.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191365123.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27503
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997243
   j =  2                              :             1377
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.68
 p-value of test no 28                 :  4.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.55
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.73
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.39
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.66
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.35
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.49
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.36
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.91
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.55
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.13
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.65
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.43
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.96
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.12
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46239
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907522
   j =  2                              :            46239
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908405
   j =  2                              :            45790
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.08
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.23
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.39
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.26
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.68
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.33
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.69
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.78
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.03
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.40
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.79
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.09
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.57
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.50
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.55
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.57
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.71
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.68
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.91
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.03
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.55
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.16
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.16
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.47
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.79
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.95
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.26
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.56
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.76
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.02
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.25
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.88
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.60
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.44
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.41
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.20
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.04
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.72
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.67
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.68
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.03
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.19
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.64
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.61
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.81
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.74
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 218                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.18
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.23
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.70
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.54
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.38
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.15
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.46
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000004357
 
 Normal statistic for number of bits   :   0.034
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.21
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999937490
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.57
 p-value of test no 238                :  5.2e-3
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:02.56
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192872451.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27504
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.33
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.11
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.90
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.82
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.28
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.27
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.93
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.29
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.63
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.62
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.64
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.33
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.38
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908289
   j =  2                              :            45851
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908041
   j =  2                              :            45978
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.26
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.91
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.74
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.20
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.81
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.13
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.23
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.29
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.00
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.05
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.80
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.79
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.22
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.70
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.08
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.29
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.84
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.64
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.23
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.86
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.29
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.84
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.44
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.15
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.59
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.28
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.68
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.19
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.37
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.21
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.75
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.59
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  446.27
 p-value of test no 169                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.34
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.98
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.14
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.26
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.07
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.52
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.38
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.92
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.89
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.45
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4713.78
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.73
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4308.31
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3796.24
 p-value of test no 228                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.02
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.93
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.96
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999966254
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.56
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000024841
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:41.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  98  HammingIndep, L=300, r=26       0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193757187.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27505
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 8                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 12                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    3.93
 p-value of test no 27                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.25
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.95
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.34
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.90
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.23
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.97
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.47
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.42
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.11
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.58
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  161.22
 p-value of test no 67                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4717.47
 p-value of test no 68                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907820
   j =  2                              :            46084
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46273
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870273
   j =  1                              :        399907458
   j =  2                              :            46265
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
 p-value of test no 113                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.74
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.71
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.90
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.75
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.20
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.39
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.70
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.08
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.66
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.15
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.51
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.51
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.38
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.36
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.70
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.92
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.80
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.65
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.18
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.55
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.05
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.46
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.07
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.71
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.61
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.27
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.27
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.00
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.23
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.95
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.74
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.20
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.86
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.65
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.22
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.20
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.49
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.81
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.14
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.55
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.09
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 217                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.88
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4664.05
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.37
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.64
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.62
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11602.72
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.87
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000097066
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.96
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000072283
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.96
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    2.44
 p-value of test no 254                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:40.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9995 
  42  Permutation, t = 7              0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194641923.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27506
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 11                 :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.74
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.94
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.70
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.72
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.12
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.32
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.36
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.88
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.91
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.62
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.84
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.11
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.08
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.64
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5258.33
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908168
   j =  2                              :            45916
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908418
   j =  2                              :            45782
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.50
 p-value of test no 119                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.42
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.44
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.28
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.65
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.14
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.80
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.81
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.71
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.66
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.08
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.03
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.49
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   43.57
 p-value of test no 150                :  4.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.91
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.06
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.05
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.84
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.82
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.10
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.49
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.69
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.78
 p-value of test no 161                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.47
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.28
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.62
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.23
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.84
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.50
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.28
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.21
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.70
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.45
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.67
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.32
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.43
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.51
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.29
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.28
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.18
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.51
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10218.71
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.74
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.20
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.74
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4274.24
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.34
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.58
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11544.52
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.53
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000111475
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.92
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000051595
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.090
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:15.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           4.5e-4
  74  RandomWalk1 C (L=50, r=0)       4.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195919875.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27507
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 5                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 12                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.61
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.31
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.71
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.38
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.78
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.52
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.42
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.90
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.08
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.48
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.22
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908139
   j =  2                              :            45929
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907743
   j =  2                              :            46121
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.64
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.21
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.74
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.79
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.29
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.41
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.28
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.54
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.55
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.76
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17170.23
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.89
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.53
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.09
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.27
 p-value of test no 150                :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.15
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.19
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.38
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.23
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.52
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.30
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.63
 p-value of test no 159                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.45
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.50
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.06
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  576.54
 p-value of test no 163                :  1.0e-2
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.26
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.66
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.83
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.04
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.18
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.97
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.00
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.87
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.94
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.10
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.14
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.66
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.87
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.02
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.57
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.61
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.96
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.37
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.27
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.14
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.43
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.36
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.26
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.56
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999951587
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.12
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999982721
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    2.51
 p-value of test no 254                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:21.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196870147.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27508
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.95
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.10
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.06
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.53
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.81
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.47
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.73
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.97
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7242.03
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.40
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.21
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.26
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.17
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908391
   j =  2                              :            45803
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907817
   j =  2                              :            46084
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-5
 p-value of test no 110                :    0.9948
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.23
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.54
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.33
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.13
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.41
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.62
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.58
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.65
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.59
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.63
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.17
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.64
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.81
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.49
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.74
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.72
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.73
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.53
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.35
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.13
 p-value of test no 156                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.86
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.29
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.69
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.31
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.05
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.05
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.94
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.55
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.65
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.73
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.56
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.97
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.53
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.23
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.44
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.37
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.46
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.82
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.43
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.34
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.32
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.02
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.82
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.23
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.35
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.64
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.95
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.69
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.70
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.65
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.50
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000076954
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.17
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000049069
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.17
 p-value of test no 249                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:38.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197984259.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27509
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.79
 p-value of test no 47                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.19
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.44
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.13
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.32
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.59
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.21
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.90
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.98
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.97
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.32
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.80
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.98
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5211.92
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46165
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870165
   j =  1                              :        399907671
   j =  2                              :            46163
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45703
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908599
   j =  2                              :            45693
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 103                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.010
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.91
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.25
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.31
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.55
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.25
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.19
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.65
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.28
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.73
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.74
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.32
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.52
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.00
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.55
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.80
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.68
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.78
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.29
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.89
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.36
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.90
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.59
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.77
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.27
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.97
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.20
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.78
 p-value of test no 165                :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.26
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.98
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.18
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.81
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.94
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.00
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.68
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.93
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.56
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.69
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.06
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.23
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.22
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
 p-value of test no 208                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10338.38
 p-value of test no 211                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.50
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.02
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.83
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.47
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.37
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.71
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.36
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.77
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999812627
 
 Normal statistic for number of bits   :   -1.48
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.35
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000029323
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.23
 p-value of test no 249                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:25.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198934531.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27510
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.02
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.93
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.48
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.72
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.25
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.48
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.51
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.96
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.19
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.01
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.19
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.98
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.85
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.49
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.74
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46424
 p-value of test no 70                 :  5.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870424
   j =  1                              :        399907153
   j =  2                              :            46422
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908064
   j =  2                              :            45962
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  7.0e-3
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.46
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.71
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.38
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.40
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.54
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.63
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.05
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.98
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 130                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.87
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.26
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.32
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.09
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.52
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.65
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.67
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.29
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.66
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.85
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.24
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.79
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.27
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.49
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.36
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.49
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.87
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.49
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.03
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.78
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.17
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.06
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.29
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.27
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.71
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.89
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.95
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.12
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.93
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.93
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.89
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.06
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.88
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.97
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.74
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.34
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.12
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.18
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.06
 p-value of test no 216                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.25
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.95
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.24
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.45
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.17
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.72
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.09
 p-value of test no 231                :  8.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999816545
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.79
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000032617
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:48.90
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199950339.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27511
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4525
 p-value of test no 17                 :  2.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    3.34
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.08
 p-value of test no 40                 :  8.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.80
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.88
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.52
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.58
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.07
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.90
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.53
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.00
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.54
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.90
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.57
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.54
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.90
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.87
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.03
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46355
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870355
   j =  1                              :        399907294
   j =  2                              :            46347
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908720
   j =  2                              :            45637
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 83                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 85                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.56
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.76
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.05
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.17
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.75
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.14
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.05
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.22
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17292.68
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.92
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.71
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.11
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.14
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.06
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.32
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.69
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.88
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.57
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.69
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.16
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.09
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.21
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.40
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.15
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.45
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.46
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.38
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.68
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.90
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.26
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  468.99
 p-value of test no 171                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.06
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.33
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.35
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.82
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 187                :  7.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 188                :    0.9974
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 3.22e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.90
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.39
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.29
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.46
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.17
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.64
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.41
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3906.22
 p-value of test no 228                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.64
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.92
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.17
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999979952
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.56
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000109540
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.90
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:16.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201129987.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27512
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997257
   j =  2                              :             1370
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 7                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 11                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.08
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.60
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.29
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.68
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.49
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.20
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.18
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.84
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.72
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.45
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.26
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.83
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  161.87
 p-value of test no 67                 :  5.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4848.23
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45582
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869582
   j =  1                              :        399908838
   j =  2                              :            45578
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907856
   j =  2                              :            46063
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.01
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.27
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.54
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.25
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.83
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.35
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.58
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.34
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.80
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17722.21
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.48
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.56
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.47
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.51
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.46
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.72
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.90
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.89
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.86
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.01
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.31
 p-value of test no 157                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.91
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.77
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.37
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.43
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.76
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.33
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.00
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.53
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.83
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.79
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.55
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.60
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.72
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.96
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.74
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.30
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.48
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.34
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.28
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.74
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.02
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.14
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.92
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.66
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.49
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.99
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.47
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.20
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.99
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.65
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.47
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.72
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999977675
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.86
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000043627
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:40.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202047491.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27513
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5613
 p-value of test no 13                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7568
 p-value of test no 19                 :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.99
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.17
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.79
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.24
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.09
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.92
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.55
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.10
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.86
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.25
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.65
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.14
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.05
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.79
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.25
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45535
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869535
   j =  1                              :        399908932
   j =  2                              :            45531
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908138
   j =  2                              :            45928
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 87                 :    0.9941
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9934
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.30
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.01
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.77
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.04
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.04
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.76
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.87
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.57
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.30
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.15
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17140.32
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.36
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.50
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.56
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.73
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.30
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.76
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.65
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.19
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.10
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.99
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.29
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.33
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.31
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.95
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.86
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.21
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.97
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.07
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.61
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.27
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.55
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.74
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.14
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.89
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.93
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.11
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.36
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.52
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.28
 p-value of test no 176                :  5.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 181                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.08
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.46
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.18
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.04
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.27
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.73
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.28
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.75
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.08
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12043.16
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.71
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000053104
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.65
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999958004
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:10.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203161603.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27514
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.54
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.89
 p-value of test no 47                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.32
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.27
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.52
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.28
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.00
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.54
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.97
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.60
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.53
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.33
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.91
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.79
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.62
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.46
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908380
   j =  2                              :            45804
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908437
   j =  2                              :            45777
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.46
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.15
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.28
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.38
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.01
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.22
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.53
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.86
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17326.57
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.65
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.24
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.40
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.74
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.54
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.89
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.15
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.95
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.25
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.09
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.09
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.68
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  187.44
 p-value of test no 164                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.88
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.81
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.85
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.42
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.12
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.17
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.88
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.68
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.79
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.33
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.55
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.90
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-4
 p-value of test no 190                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.08
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.01
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.35
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.35
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10208.10
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
 p-value of test no 212                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10352.14
 p-value of test no 215                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.11
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.93
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.53
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.85
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.75
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.44
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.62
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000062119
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.16
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999911720
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:56.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204210179.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27515
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.46
 p-value of test no 29                 :  5.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.09
 p-value of test no 40                 :  8.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.91
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.19
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.59
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.55
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.55
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.70
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.36
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.91
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.16
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.96
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.32
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.04
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.05
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.43
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45488
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869488
   j =  1                              :        399909026
   j =  2                              :            45484
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46148
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870148
   j =  1                              :        399907708
   j =  2                              :            46140
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.44
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.30
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.87
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.68
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.04
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.44
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.11
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.95
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.61
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 142                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17859.34
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.68
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.93
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.00
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.51
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.33
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.34
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.44
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.10
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.22
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.15
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.93
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.61
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.66
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.64
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.44
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.92
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.59
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.45
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.86
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.71
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.97
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.84
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.04
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.08
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.98
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.39
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.41
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.00
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.35
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.10
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.40
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.34
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.29
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 225                :    0.9996    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.00
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.58
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.40
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.83
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12078.43
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.73
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000142891
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.33
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999940610
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    3.10
 p-value of test no 244                :  9.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:14.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205520899.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27516
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1237
 p-value of test no 3                  :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334357
   j =  1                              :        599997526
   j =  2                              :             1237
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5528
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.78
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.74
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.97
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.42
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.79
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.92
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.24
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.30
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.64
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.22
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.64
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4890.47
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908308
   j =  2                              :            45834
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908265
   j =  2                              :            45863
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.45
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.12
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.25
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.18
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.25
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.38
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.38
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.35
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.59
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.54
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.80
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.04
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.21
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.19
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.17
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.71
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.31
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.63
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.59
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.72
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.51
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.42
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.33
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.64
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.64
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.86
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.84
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.46
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.88
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.68
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.36
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.34
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.98
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.72
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.24
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.74
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.66
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.10
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.65
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.45
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.20
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.18
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.33
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.80
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 212                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10258.30
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.19
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.03
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.87
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.77
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.61
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.50
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.15
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999923873
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.13
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000031849
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:24.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206602243.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27517
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    3.18
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     188
 p-value of test no 43                 :  1.5e-3
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.13
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.77
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.03
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  184.30
 p-value of test no 54                 :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.78
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.46
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.08
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.15
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.11
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.44
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.89
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907962
   j =  2                              :            46010
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908188
   j =  2                              :            45906
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.45
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.91
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.21
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.32
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.00
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.81
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.96
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
 p-value of test no 138                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.24
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.55
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.80
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.34
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.94
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.03
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.25
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.77
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.32
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.56
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.33
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.50
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.05
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.04
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.65
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.49
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.43
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.98
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.85
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.38
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.60
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.02
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.00
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.02
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.41
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.57
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.99
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.58
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.48
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.70
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.76
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.51
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.73
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10237.55
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.36
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.53
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.39
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.61
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11535.86
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.52
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.71
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000091450
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.07
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999992207
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:04.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207650819.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27518
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5583
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   24.99
 p-value of test no 46                 :  7.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.48
 p-value of test no 47                 :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.00
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.34
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.82
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.06
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.77
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1341.75
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.38
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.68
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.23
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.90
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.67
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45517
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869517
   j =  1                              :        399908969
   j =  2                              :            45511
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908834
   j =  2                              :            45577
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.95
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.81
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.39
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.62
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.01
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.51
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.55
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.82
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.09
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.66
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.84
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.85
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.65
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.28
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.16
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.54
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.32
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.67
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.20
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.56
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.99
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.06
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.87
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.22
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.62
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.50
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.05
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.67
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.91
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.11
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.91
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.38
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.28
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.19
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.89
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.79
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.87
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.42
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.35
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.68
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.63
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.35
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.91
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.18
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.65
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.81
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.40
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.12
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.08
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999934724
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.13
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000128791
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:48.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                7.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208666627.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27519
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7124
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     539
 p-value of test no 31                 :    0.9939
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.85
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.54
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.81
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.81
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.18
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.14
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.34
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.15
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.78
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.62
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.07
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.76
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.60
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46251
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870251
   j =  1                              :        399907502
   j =  2                              :            46243
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908608
   j =  2                              :            45693
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.66
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.76
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.33
 p-value of test no 121                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.17
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.43
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.83
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.77
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.02
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.34
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.74
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.13
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.17
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.98
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.46
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.56
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.02
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.29
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.57
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.11
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.94
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.07
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.90
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.47
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.99
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.31
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.09
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.46
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.45
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.51
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.74
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.66
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.00
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.61
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.14
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.40
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.09
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.45
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.17
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.78
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.49
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.22
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.72
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.16
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.28
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.68e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.73
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.91
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.08
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.65
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.28
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.93
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.19
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999906437
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.55
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000053962
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 250                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 251                :    0.9914
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:57:12.80
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209682435.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27520
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.65
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.86
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.27
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.26
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.77
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.78
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.26
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.18
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.68
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.76
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.78
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.35
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.68
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.59
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.33
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.87
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908092
   j =  2                              :            45951
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907840
   j =  2                              :            46080
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 76                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 83                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 92                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.08
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.09
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.84
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.62
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.43
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.97
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.66
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.36
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.93
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.99
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.65
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.25
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.45
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.21
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.68
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.27
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.26
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.71
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.20
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.60
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.66
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.58
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.15
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.50
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.72
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.72
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.71
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.59
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.87
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.90
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.58
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.96
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.13
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.21
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.04
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.25
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.03
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.44
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.86
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.86
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.21
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.39
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.31
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.22
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.88
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.79
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.32
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.98
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.76
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.32
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.96
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.74
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.97
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.53
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999965450
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.27
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999889865
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 235                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:38.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189005828.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27521
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.61
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.24
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.55
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.26
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.86
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.51
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.64
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.41
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.05
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.01
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.03
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.70
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.40
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908507
   j =  2                              :            45739
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908370
   j =  2                              :            45812
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9905
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.10
 p-value of test no 118                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.46
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.13
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.70
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.11
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.81
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.21
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.23
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.78
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.75
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.60
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.84
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.82
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.79
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.24
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.48
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.90
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.34
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.57
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.65
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.28
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.64
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.80
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.32
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.35
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.99
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.75
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.41
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.96
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.85
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.42
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.93
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.05
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.31
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.24
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.04
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.37
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.34
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.67
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.82
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.65
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.47
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.60
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.73
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.83
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.22
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.24
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.00
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.42
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.72
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.22
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.96
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.88
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999831074
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.84
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000109381
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:43.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  58  AppearanceSpacings, r = 27      0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190349316.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27522
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1212
 p-value of test no 11                 : 1 -  1.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334332
   j =  1                              :        599997576
   j =  2                              :             1212
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.80
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.83
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.98
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.38
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.72
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.66
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.98
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.31
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.74
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.43
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.32
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.22
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.85
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.11
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.36
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.51
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.87
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908722
   j =  2                              :            45627
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908253
   j =  2                              :            45866
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 95                 :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  2.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 115                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.89
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.07
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.48
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.79
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.56
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.77
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.00
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.28
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.64
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.38
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.05
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.74
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.35
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.23
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.50
 p-value of test no 152                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.22
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.99
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.60
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.52
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.25
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.24
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.64
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.15
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.29
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.57
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.74
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.01
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.72
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.91
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.88
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.89
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.76
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.40
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.01
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.16
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.86
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.57
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.31
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.87
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.14
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.68
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.91
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.28
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.95
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.98
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.14
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.82
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11556.55
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.75
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.66
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000020995
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999913688
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:49.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  1.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191528964.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27523
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    3.97
 p-value of test no 38                 :  9.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    4.82
 p-value of test no 42                 :  3.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.11
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.57
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.28
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.10
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.28
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.50
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.88
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.74
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.34
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.96
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.55
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.51
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.23
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.56
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907861
   j =  2                              :            46065
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908291
   j =  2                              :            45850
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-4
 p-value of test no 110                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.20
 p-value of test no 111                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.53
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.84
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.26
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.68
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.25
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.05
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.83
 p-value of test no 133                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.29
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.91
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.59
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.68
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.52
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.33
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.60
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.60
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.57
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.81
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.31
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.49
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.45
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.57
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.21
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.06
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.20
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.88
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.83
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.51
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.17
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.33
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.00
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.09
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.54
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.67
 p-value of test no 172                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.85
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.70
 p-value of test no 174                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.91
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.84
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 194                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.17
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.59
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.50
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.49
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.91
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.55
 p-value of test no 217                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.89
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.95
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.39
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.12
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.94
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.71
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.96
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999935618
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.53
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999916859
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9916
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:26.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192217092.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27524
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 12                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.17
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.58
 p-value of test no 48                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.64
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.18
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.87
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.61
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.02
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.68
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.38
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.49
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.06
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.83
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.29
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908290
   j =  2                              :            45849
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908273
   j =  2                              :            45862
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 80                 :  2.6e-3
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 81                 :  8.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  8.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
 p-value of test no 103                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.97
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.77
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.77
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.62
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.80
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.73
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.62
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.41
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.71
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.39
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17163.50
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.99
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.40
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.21
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.80
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.28
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.10
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.59
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.40
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.74
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.17
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.09
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.92
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.12
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.88
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.80
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.62
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.17
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.44
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.62
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.85
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.49
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.21
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.88
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.30
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.11
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.28
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.13
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.50
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.53
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.59
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.85
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.77
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.61
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.23
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.73
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.45
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.63
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12013.83
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.56
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.35
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999946457
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.68
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000031513
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:47.82
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193167364.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27525
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 4                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     549
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.41
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.22
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.99
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.82
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.01
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.81
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.65
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.57
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.04
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.39
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.49
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.12
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.19
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907818
   j =  2                              :            46088
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45519
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908966
   j =  2                              :            45511
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.05
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.47
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.77
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.75
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.08
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.83
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.20
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.15
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.10
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.32
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.90
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.94
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.10
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.86
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.15
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.58
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.31
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.59
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.75
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.21
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.01
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.37
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.23
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.64
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.61
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.08
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.54
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.73
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.81
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.11
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.78
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.04
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.03
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.41
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.98
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.56
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.62
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.03
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.12
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.51
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.65
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.45
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.16
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.16
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3918.60
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.80
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.88
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000009847
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.55
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999962159
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 253                :    0.28
 
 Sample variance                       :    2.11
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:18.30
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194215940.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27526
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9935
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.20
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.81
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.33
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.86
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.00
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.39
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.28
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.79
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.78
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.26
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.59
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4691.82
 p-value of test no 68                 :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908619
   j =  2                              :            45689
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46205
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870205
   j =  1                              :        399907593
   j =  2                              :            46199
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 86                 :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.75
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.08
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.43
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.79
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.61
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.75
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.74
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.51
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17292.08
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.39
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.20
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.27
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.79
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.19
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.21
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.60
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.66
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.38
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.17
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.27
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.45
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.73
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.57
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.63
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.59
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.47
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.14
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4789.19
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.50
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.95
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.14
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.73
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.32
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.79
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.92
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    2.20
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.87
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.78
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.27
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9790.08
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.09
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.96
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.67
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.50
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.04
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.31
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.37
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.91
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999959846
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.48
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000116371
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    2.13
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:09.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195198980.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27527
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.09
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.98
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.03
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.75
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.08
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.97
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.74
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.11
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.72
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7350.05
 p-value of test no 57                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.46
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.06
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.73
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.29
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.66
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908383
   j =  2                              :            45804
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908185
   j =  2                              :            45900
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.38
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.27
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.20
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.07
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.81
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.81
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.28
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.76
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.91
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.62
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.83
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17020.56
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.87
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.07
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.53
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.95
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.51
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.55
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.72
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.22
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.25
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.68
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.91
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.45
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.50
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.00
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.40
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.99
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.51
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.13
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.75
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.97
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.16
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.70
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.04
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.18
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.94
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.57
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.37
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.66
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.19
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.18
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.18
 p-value of test no 189                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.36
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.24
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.85
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9726.33
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.44
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.45
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.73
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.85
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.17
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.85
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.07
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.15
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000101725
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.28
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999817844
 
 Normal statistic for number of bits   :   -1.44
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:16.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196214788.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27528
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 9                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7561
 p-value of test no 15                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.38
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.89
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.40
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.92
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.01
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.90
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.05
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.38
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.78
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.81
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.22
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.16
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4801.95
 p-value of test no 68                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908456
   j =  2                              :            45766
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46218
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870218
   j =  1                              :        399907568
   j =  2                              :            46210
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.79
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.23
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.26
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.21
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.70
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.02
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.32
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.43
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.20
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17187.89
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.23
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.66
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.66
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.06
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.87
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.50
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.54
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.97
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.37
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.90
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.63
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.19
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.75
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.12
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.40
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.62
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.88
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.49
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.03
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.55
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.36
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.59
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.01
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.18
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.88
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.08
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.90
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.58
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.50
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.60
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.03
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.40
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.28
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.79
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.36
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.14
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.68
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.28
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999987485
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999886160
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.078
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:49.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197328900.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27529
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.40
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.32
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.53
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.24
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.31
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.26
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.82
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.83
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.36
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.62
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.66
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.74
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.35
 p-value of test no 66                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.85
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5230.54
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46150
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907702
   j =  2                              :            46146
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.15
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.18
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.55
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.02
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.96
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.86
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.82
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.42
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.98
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.34
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.68
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.78
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.96
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.82
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.40
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.17
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.89
 p-value of test no 154                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.27
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.57
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.65
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.72
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.10
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.11
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.34
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.93
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.59
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  307.05
 p-value of test no 166                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.71
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.04
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.54
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.90
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.35
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.69
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.43
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.73
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.82
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.46
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.78
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.51
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.55
 p-value of test no 198                :    0.9918
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.10
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.46
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.19
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.73
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.20
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.67
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.20
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.61
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.87
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.41
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.69
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000042232
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.63
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999974837
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:44.98
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198377476.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27530
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4547
 p-value of test no 14                 :  7.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.14
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.49
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.27
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.66
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.65
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.74
 p-value of test no 53                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.50
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.96
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.97
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.88
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.58
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.45
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.75
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.99
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.83
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907729
   j =  2                              :            46134
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46278
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870278
   j =  1                              :        399907449
   j =  2                              :            46268
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.25
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.45
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.13
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.40
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.42
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.57
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.01
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.64
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.19
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17552.01
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.06
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.45
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.72
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.56
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.60
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.90
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.28
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.63
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.40
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.40
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.79
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.75
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.88
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.35
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.08
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.95
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.29
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.30
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.49
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.84
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.91
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.34
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.69
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.67
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.52
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.35
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.24
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.06
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.06
 p-value of test no 176                :  3.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.30
 p-value of test no 177                :    0.9995    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.31
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.40
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.22
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.36
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.44
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.35
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.68
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.47
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.90
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.44
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.96
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.49
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.40
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000065404
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.37
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999920864
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:31.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         7.8e-4
  80  LinearComp, r = 0               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199393284.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27531
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.33
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.05
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.85
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.96
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.44
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.44
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.43
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.89
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.83
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.73
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.68
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.91
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.99
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.61
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.98
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908459
   j =  2                              :            45766
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908147
   j =  2                              :            45925
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 72                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 98                 :    0.9938
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.29
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.15
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.25
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.30
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.07
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.61
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.00
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.20
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.43
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.05
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.87
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.11
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.03
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.85
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.59
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.82
 p-value of test no 154                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.87
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.67
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.33
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.00
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.85
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.09
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.11
 p-value of test no 161                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.47
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.55
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.14
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.20
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.77
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.07
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.74
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.56
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.12
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.46
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.31
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.69
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.46
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.36
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 194                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.16
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.02
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.32
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.37
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.51
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.07
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5136.31
 p-value of test no 226                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.83
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.50
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12180.24
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12132.53
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.62
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000020608
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.49
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999798080
 
 Normal statistic for number of bits   :   -1.60
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.029
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:59.46
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200409092.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27532
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 7                  :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.96
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.79
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.44
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.39
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.97
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.82
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.84
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.46
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.93
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6744.79
 p-value of test no 57                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.94
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.80
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.68
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.44
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.80
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908897
   j =  2                              :            45544
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908375
   j =  2                              :            45805
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.19
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.56
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.40
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.58
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.45
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.83
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.70
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.08
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17495.58
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.83
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.19
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.54
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.93
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.60
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.62
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.32
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.18
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.68
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.68
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.44
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.05
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.36
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.14
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.31
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.77
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.25
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.90
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.00
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.28
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.28
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.19
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.20
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.07
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.64
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.67
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.92
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.56
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.36
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.17
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-4
 p-value of test no 205                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.77
 p-value of test no 207                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 210                :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9643.05
 p-value of test no 211                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.55
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.87
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.94
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.38
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.83
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.34
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.62
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.79
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999883646
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.09
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000000700
 
 Normal statistic for number of bits   : 5.53e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:53.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201457668.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27533
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.29
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.11
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.94
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.32
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.56
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6849.69
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.92
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.25
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.47
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.64
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.36
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907854
   j =  2                              :            46064
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907524
   j =  2                              :            46232
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.74
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.77
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.25
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.09
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.66
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.02
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.68
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.64
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.19
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17241.86
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.44
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.19
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.83
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.42
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.61
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.05
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.97
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.82
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.27
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.27
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.11
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.15
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.65
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.29
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.69
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.12
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.82
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.29
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.21
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.74
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.29
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.89
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.72
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.12
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.81
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.74
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.24
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.00
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.88
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.80
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.03
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.95
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.26
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9665.47
 p-value of test no 211                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.83
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.19
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.83
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4309.65
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.28
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.44
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11555.71
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.17
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000069853
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.94
 p-value of test no 233                :    0.9968
 
 
 -----------------------------------------------
 Total number of bits:  7999909245
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:09.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202506244.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27534
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5575
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7096
 p-value of test no 18                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7557
 p-value of test no 21                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.18
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.20
 p-value of test no 48                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.81
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.78
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.83
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.83
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.54
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.20
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.70
 p-value of test no 61                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.44
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.27
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.60
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.05
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908232
   j =  2                              :            45881
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908148
   j =  2                              :            45923
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 86                 :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.21
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.56
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.27
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.50
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.43
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.95
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.54
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.69
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.94
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.16
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.08
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.36
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.56
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.66
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.19
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.74
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.52
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.06
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.47
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.05
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.86
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.92
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.76
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.97
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.08
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.06
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.16
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.48
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.19
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.03
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.19
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.83
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.17
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.40
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.74
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.21
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.42
 p-value of test no 188                :  7.7e-3
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.58
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.34
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.27
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.64
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.49
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 219                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    5.12
 p-value of test no 221                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4593.69
 p-value of test no 222                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.07
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.89
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.97
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.43
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11575.70
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.36
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999930296
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.87
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999916196
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:30.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203554820.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27535
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.00
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.09
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    6.41
 p-value of test no 44                 :  6.4e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.50
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.37
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.82
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.58
 p-value of test no 50                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.12
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.46
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1611.28
 p-value of test no 56                 :  8.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.37
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.68
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.87
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.08
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.22
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5180.61
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908509
   j =  2                              :            45741
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46178
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870178
   j =  1                              :        399907651
   j =  2                              :            46164
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.36
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.31
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.31
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.11
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.78
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.46
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.15
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17765.27
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.87
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.03
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.35
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.91
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.45
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.40
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.12
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.80
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.21
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.68
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.38
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.31
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.05
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.76
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.15
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.21
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.77
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.06
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.29
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.16
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.00
 p-value of test no 172                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.33
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.01
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.41
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.52
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.17
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    2.26
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.39
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.18
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.03
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.02
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9770.35
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.74
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.18
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.59
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.88
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.56
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.28
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.37
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000023245
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.71
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000085279
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:38.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         6.4e-4
  36  Gap, r = 0                      8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204603396.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27536
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.52
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.09
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.25
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.11
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.13
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.52
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  171.35
 p-value of test no 54                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.33
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.31
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.80
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.23
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.35
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.34
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.60
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46161
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870161
   j =  1                              :        399907681
   j =  2                              :            46155
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45441
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869441
   j =  1                              :        399909122
   j =  2                              :            45433
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.44
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.48
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.42
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.35
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.71
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.77
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.72
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.45
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17714.11
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.14
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.05
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.42
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.09
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.63
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.76
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.04
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.57
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.26
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.77
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.44
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.70
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.33
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.53
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.90
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.77
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.74
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.00
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.52
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.16
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.52
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5233.26
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.37
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.08
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.59
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.03
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.89
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.18
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.09
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.09
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-4
 p-value of test no 181                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 182                :  6.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.07
 p-value of test no 183                :    0.9989
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.27
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 200                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  267.74
 p-value of test no 203                :  9.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.81
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.98
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.84
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.84
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.14
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.70
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.03
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.01
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.49
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.31
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999982367
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.63
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999933671
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    2.42
 p-value of test no 239                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:01.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  88  PeriodsInStrings, r = 0         9.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205651972.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27537
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4199
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.94
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.41
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.84
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.70
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.40
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.78
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.78
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.01
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.53
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.21
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.88
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.50
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.45
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4867.39
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908586
   j =  2                              :            45698
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46174
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870174
   j =  1                              :        399907655
   j =  2                              :            46168
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.00
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.40
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.28
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.63
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.38
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.67
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.37
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 131                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.97
 p-value of test no 133                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.50
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.66
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.97
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.66
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.97
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.05
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.99
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.87
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.98
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.72
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.89
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.04
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.23
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.74
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.35
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.97
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.25
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.77
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.39
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.36
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.60
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.48
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.19
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.15
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.59
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.68
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.51
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.90
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.49
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.46
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.09
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.50
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.42
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.60
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.42
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.38
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.46
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.92
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.45
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 225                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4632.29
 p-value of test no 226                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.42
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.44
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.25
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.40
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.15
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000144220
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.10
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999940895
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.46e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:54.31
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206700548.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27538
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 7                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 11                 :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.15
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.14
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.70
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.83
 p-value of test no 50                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.57
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.60
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.48
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.69
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1347.78
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.38
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.31
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.57
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.11
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.64
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908630
   j =  2                              :            45682
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907866
   j =  2                              :            46055
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.53
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.24
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.12
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.60
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.70
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.85
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.67
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.12
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.46
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 139                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 140                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.66
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17598.39
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.41
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.84
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.40
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.54
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.34
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.42
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.35
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.86
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.58
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.65
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.61
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.04
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.82
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.98
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.04
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.56
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.27
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.14
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.26
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.56
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.38
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.36
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.91
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.81
 p-value of test no 170                :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.09
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.70
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.34
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.07
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.80
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.89
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   34.00
 p-value of test no 178                :  6.7e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.53
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.56
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.60
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.68
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.18
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.50
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.14
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.79
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.75
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.70
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.00
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000052777
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.66
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000038317
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 246                :    0.9916
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:04.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 0               6.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207749124.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27539
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.9906
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.52
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   22.37
 p-value of test no 47                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.70
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.35
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.37
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.92
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.22
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.53
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.56
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.94
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7266.59
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.55
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.12
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.17
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.76
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4824.70
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908518
   j =  2                              :            45732
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908424
   j =  2                              :            45782
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.41
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.92
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.08
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.48
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.83
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.45
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.27
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.45
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.95
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.87
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.60
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.02
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.53
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.91
 p-value of test no 151                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.17
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.01
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.08
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.12
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.81
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.34
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.58
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.55
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.62
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.31
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.54
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.91
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.76
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.77
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.56
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.44
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.46
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.32
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.35
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.13
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.98
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.20
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.37
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.22
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.98
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.85
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.86
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.29
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.69
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4670.08
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.10
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.04
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.04
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.45
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.38
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.07
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999843482
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.74
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000050659
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.19
 p-value of test no 239                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:11.98
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208863236.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27540
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.15
 p-value of test no 23                 :  2.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 41                 :    0.9970
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.30
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.13
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.36
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.94
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.70
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.27
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.17
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.71
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.33
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.89
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.74
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908293
   j =  2                              :            45849
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908518
   j =  2                              :            45735
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.46
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.88
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.39
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.04
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.99
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.29
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.87
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.74
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.10
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17202.65
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.82
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.45
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.97
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.41
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.01
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.51
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.08
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.33
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.47
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.67
 p-value of test no 158                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.55
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.90
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.16
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.82
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.87
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.59
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.23
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.47
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.68
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.26
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.03
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.89
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.86
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.34
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.60
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.48
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.60
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.19
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 181                :    0.9942
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.09
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.59
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.97
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.54
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9713.59
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.63
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.53
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.16
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.45
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.60
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.62
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.91
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.09
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999905159
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.47
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999936944
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:36.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189038597.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27541
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.68
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.02
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.84
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.30
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.22
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.56
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.37
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.27
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.70
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7244.82
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.48
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.99
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.67
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.08
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908542
   j =  2                              :            45717
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908427
   j =  2                              :            45779
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.59
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.22
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.26
 p-value of test no 123                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.59
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.89
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.88
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.26
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.91
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.19
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.54
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.54
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.32
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.02
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.24
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.39
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.41
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.85
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.04
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.21
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.47
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.78
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.77
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.18
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.70
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.72
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.92
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.82
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.44
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.11
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.31
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.03
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.43
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.55
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.81
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.35
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.24
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.35
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.21
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.72
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    2.44
 p-value of test no 184                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.37
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.40
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10208.41
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.38
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.95
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.47
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.22
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.80
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.53
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.38
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.01
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000041572
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.54
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000187381
 
 Normal statistic for number of bits   :    1.48
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:48.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190251013.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27542
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.68
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.62
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.92
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.18
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.37
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.57
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.34
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.84
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.45
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.53
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.49
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.66
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.35
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908203
   j =  2                              :            45894
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908289
   j =  2                              :            45851
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.07
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.57
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.19
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.90
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.03
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.78
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.99
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.58
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.79
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.98
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.56
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.24
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.44
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.84
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.02
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.85
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.08
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.12
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.60
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.58
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.85
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.96
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.09
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.65
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.27
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.43
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.45
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.62
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.68
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.16
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.45
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.21
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.45
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.83
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.61
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.28
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.14
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.50
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.87
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.22
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.78
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.82
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 220                :    0.9905
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4640.73
 p-value of test no 222                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.68
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.15
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.66
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.08
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.53
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.41
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999851354
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.43
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000196111
 
 Normal statistic for number of bits   :    1.55
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 248                :    0.54
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.100
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:40.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191758341.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27543
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9947
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.67
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.22
 p-value of test no 47                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.88
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.31
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.90
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.33
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.06
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.18
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.82
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.03
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7181.82
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.58
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.22
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.54
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.82
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908156
   j =  2                              :            45913
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908509
   j =  2                              :            45744
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-3
 p-value of test no 104                :    0.9982
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 105                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.96
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.44
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.96
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.13
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.25
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.25
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.53
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.11
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.45
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.54
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.11
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.34
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.36
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.19
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.90
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.52
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.31
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.25
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.12
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.80
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.12
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.06
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.18
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.27
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.40
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.01
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.27
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.34
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.96
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.36
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.42
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.42
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.45
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.04
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.72
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.38
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.72
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.94
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.87
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.99
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.51
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.58
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.81
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.25
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.24
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.62
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.98
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.00
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.53
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.26
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.90
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.31
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.07
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000027358
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.59
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000003883
 
 Normal statistic for number of bits   :   0.031
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:37.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192708613.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27544
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.9912
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.70
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9916
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.12
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.05
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.94
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.82
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.61
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.77
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.00
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.53
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.41
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.08
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.33
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.82
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.12
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.37
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907986
   j =  2                              :            46001
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908196
   j =  2                              :            45896
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-4
 p-value of test no 98                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 103                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.59
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.09
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.37
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.82
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.70
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.26
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.51
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.39
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.40
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.23
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17350.79
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.88
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.43
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.32
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.55
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.31
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.32
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.17
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.23
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.62
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.46
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.05
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.62
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.30
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.85
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.63
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.53
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.93
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.80
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.46
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.36
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.06
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.75
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.45
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.39
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.55
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.89
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.91
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.60
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.95
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.09
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9750.40
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.76
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.06
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.45
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.45
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.48
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11617.63
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.83
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.16
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999983816
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.79
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999973133
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:43.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193626117.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27545
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.98
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.50
 p-value of test no 48                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.28
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.76
 p-value of test no 52                 :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.42
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.34
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.79
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7276.53
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.22
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.93
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.11
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.14
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907878
   j =  2                              :            46058
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 86                 :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-6
 p-value of test no 112                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.36
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.16
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.89
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.83
 p-value of test no 123                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.16
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   10.10
 p-value of test no 125                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.68
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 130                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.69
 p-value of test no 133                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.09
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.93
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.76
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.59
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.94
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.27
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.37
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.71
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.79
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.19
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.45
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.13
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.42
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.36
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.93
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.26
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.71
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.69
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.55
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.91
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.22
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.98
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.78
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  461.72
 p-value of test no 169                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.61
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.60
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.54
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.70
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.60
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.67
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.46
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.96
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.05
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.26
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.62
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.78
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.69
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.62
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.73
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.41
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.83
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.24
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.15
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.58
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999986822
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.27
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000132484
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    2.29
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:57.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194936837.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27546
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 23                 :    0.9972
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.35
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.26
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.85
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.67
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.94
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.43
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.92
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.18
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.12
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.43
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.54
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.12
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.30
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908250
   j =  2                              :            45872
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908261
   j =  2                              :            45862
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.62
 p-value of test no 116                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.54
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.16
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.86
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.40
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.81
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.01
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.87
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.96
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.43
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17216.38
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.07
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.87
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.56
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.91
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.98
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.98
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.92
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.81
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.03
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  579.48
 p-value of test no 158                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.23
 p-value of test no 159                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.35
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.25
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.82
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.12
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.33
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.57
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.89
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.83
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.89
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.73
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.59
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.47
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.80
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.25
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.21
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.13
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.26
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.43
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.39
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.97
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.14
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.20
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.98
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.89
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.96
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.28
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.85
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.18
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.11
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999804095
 
 Normal statistic for number of bits   :   -1.55
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.08
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000013297
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:13.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196182021.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27547
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 9                  :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.62
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.91
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.71
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.18
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.17
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.57
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.94
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.94
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.09
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.35
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.62
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.07
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.69
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.82
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908318
   j =  2                              :            45835
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908545
   j =  2                              :            45720
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -9.36e-5
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.38
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.31
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.46
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.51
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.31
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.85
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.13
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.15
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.92
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.15
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17608.38
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.06
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.66
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.22
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.51
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.02
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.62
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.50
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.51
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.15
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.14
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.32
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.16
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.51
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.04
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.69
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.85
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.81
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.58
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.80
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.50
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.81
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.72
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.76
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.11
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.19
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.52
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.24
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.68
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.92
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.05
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.57
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.10
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.44
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.94
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5152.85
 p-value of test no 226                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.85
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.52
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.06
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.15
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.21
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000103132
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.91
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999988922
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:07.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197230597.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27548
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.95
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.99
 p-value of test no 47                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.97
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.75
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.34
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.65
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.77
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.00
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.06
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.66
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.46
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.15
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.02
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.59
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.34
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45348
 p-value of test no 70                 :    0.9935
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869348
   j =  1                              :        399909308
   j =  2                              :            45340
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46186
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907630
   j =  2                              :            46182
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.69
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.14
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.20
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.87
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.17
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.62
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.74
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.44
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.29
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.75
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.40
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.39
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.35
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.09
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.64
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.84
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.59
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.54
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.19
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.91
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.39
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.14
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.38
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.23
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.71
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.54
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.44
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.44
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.76
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.79
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.78
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.92
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.03
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.67
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.35
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.05
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.74
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.69
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.94
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.93
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.02
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.23
 p-value of test no 184                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.73
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.01
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.82
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.96
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.25
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4658.11
 p-value of test no 222                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.29
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.98
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.38
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.75
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.81
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.92
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000096016
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.99
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999881147
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:21.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198180869.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27549
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     816
 p-value of test no 25                 :    0.9976
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    3.49
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.22
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.38
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.37
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.03
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.93
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.68
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.90
 p-value of test no 53                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.46
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.12
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.00
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.80
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.38
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.50
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.89
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.56
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.03
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907955
   j =  2                              :            46015
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908086
   j =  2                              :            45951
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  8.8e-3
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 106                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 118                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.52
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.21
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.67
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.94
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.53
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.38
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.03
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.95
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.32
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.41
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17641.14
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.68
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.95
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.40
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.44
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.33
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.42
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.95
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.46
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.89
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.75
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.74
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.52
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.20
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.34
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.16
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.08
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.08
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.54
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.39
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.15
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.82
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.71
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.14
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.03
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.40
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.98
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.39
 p-value of test no 177                :  8.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.10
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.73
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.86
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.95
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.64
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.86
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 219                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.88
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.20
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.46
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.52
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.02
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.13
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.24
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999864299
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.68
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999974879
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:58.44
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199294981.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27550
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.82
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.36
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    5.35
 p-value of test no 42                 :  2.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     112
 p-value of test no 43                 :    0.9993    *****
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.96
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.77
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.07
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.86
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.59
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.01
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.13
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.70
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.85
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.42
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.35
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.25
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.64
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908514
   j =  2                              :            45734
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45547
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869547
   j =  1                              :        399908908
   j =  2                              :            45543
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.72
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.10
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.61
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.22
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.58
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.09
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.23
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 139                :    0.9938
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   95.74
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.66
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.89
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.83
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.18
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.37
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.83
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.64
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.15
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.81
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.92
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.41
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.85
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.08
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.04
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.90
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.21
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.84
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.57
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.45
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.04
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.49
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.14
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.34
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.21
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.68
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.95
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.90
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.60
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.43
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.64
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.85
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.98
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.87
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.91
 p-value of test no 217                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.21
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.95
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.87
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.01
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.57
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.96
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.26
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999817166
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.17
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000121741
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.017
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:25.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200278021.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27551
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 5                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.52
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.79
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.38
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.16
 p-value of test no 50                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.55
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.93
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.14
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.44
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6824.12
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.34
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.66
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.07
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4871.75
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46260
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870260
   j =  1                              :        399907484
   j =  2                              :            46252
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 5.88e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.72
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.80
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.62
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.88
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.64
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.65
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.74
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.79
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.68
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.84
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.24
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.94
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.46
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.97
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.55
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.09
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.36
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.58
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.23
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.73
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.28
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.27
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.29
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.95
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.73
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.97
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.70
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.29
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.81
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.63
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.00
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.77
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.42
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.21
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.54
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.52
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.02
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.73
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.40
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.00
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.62
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.50
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.14
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10260.41
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.27
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.51
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.02
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.93
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.16
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.61
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.15
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999804632
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.04
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000108925
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.42
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201293829.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27552
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 10                 :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9977
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.67
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.18
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.15
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.06
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.74
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.76
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.32
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.66
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.62
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.39
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.30
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.82
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.54
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.28
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  3.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908262
   j =  2                              :            45860
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908409
   j =  2                              :            45791
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.92
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.80
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.29
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.10
 p-value of test no 122                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.83
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.03
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.50
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.92
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.04
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.89
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.09
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.38
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.20
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.38
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.25
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.05
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.50
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.38
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.64
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.40
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.20
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.92
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.69
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.74
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.14
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.25
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.87
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.41
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.86
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.57
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.47
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.48
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.30
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.05
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.24
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.08
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.72
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.67
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.87
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.32
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.78
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.42
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.89
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5126.49
 p-value of test no 226                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.61
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.76
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.22
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.78
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.07
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999929612
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.21
 p-value of test no 233                :  6.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000028915
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:20.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  43  Permutation, t = 10             3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202211333.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27553
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 11                 :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.03
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.20
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.08
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.43
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.20
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.18
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.21
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.99
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.20
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6904.98
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.87
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.54
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.25
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5211.50
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908269
   j =  2                              :            45861
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908299
   j =  2                              :            45843
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.18
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.74
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.63
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.40
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.65
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.15
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.09
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.87
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.14
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.96
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.39
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.69
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.25
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.41
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.39
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.11
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.98
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.79
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.78
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.43
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.21
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.11
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   84.36
 p-value of test no 164                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.66
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.24
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.11
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.11
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.28
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.55
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.64
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.74
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.18
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.56
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.63
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.47
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.98
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.78
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.50
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 214                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.80
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.32
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.04
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.60
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.25
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.58
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.11
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.73
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000085627
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.10
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000036472
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:53.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           4.5e-4
  77  RandomWalk1 R (L=1000, r=20)    0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203227141.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27554
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 10                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5301
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.23
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.35
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.52
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.33
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.23
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.49
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.54
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.69
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.42
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.57
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.85
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.75
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6858.91
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.24
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.60
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.22
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.98
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.32
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908240
   j =  2                              :            45874
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908466
   j =  2                              :            45761
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.12
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.61
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.69
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.18
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.83
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.05
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.61
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.12
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.85
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.50
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.25
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.32
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.45
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.80
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.86
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.53
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.52
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.22
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.55
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.63
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.28
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.81
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.92
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.44
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.46
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.87
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.91
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.20
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.61
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.92
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.48
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.04
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.71
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.22
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.44
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.27
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.13
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-4
 p-value of test no 190                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.43
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.60
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.26
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.26
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.41
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.27
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.30
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.74
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.36
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.75
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.57
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999977642
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.97
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999981743
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:28.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204374021.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27555
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1244
 p-value of test no 3                  :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334364
   j =  1                              :        599997512
   j =  2                              :             1244
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    3.60
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.26
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.22
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.95
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.24
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.61
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.19
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.02
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.82
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.36
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.02
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.30
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.16
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908888
   j =  2                              :            45556
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908398
   j =  2                              :            45798
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 115                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.28
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.34
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.01
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.42
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.02
 p-value of test no 123                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.18
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.48
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.97
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.05
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.31
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.03
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.69
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.48
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.61
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.20
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.07
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.79
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.72
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.40
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.95
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.22
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.26
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.29
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.91
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.47
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.23
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.33
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.41
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.45
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.85
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.88
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.20
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.46
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.96
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.84
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.95
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.79
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.12
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.12
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.75
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.23
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.13
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.86
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.25
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.65
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4303.56
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3966.81
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.44
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.47
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.98
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000104908
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.42
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999979985
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 241                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 242                :  5.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.84
 p-value of test no 243                :  2.3e-3
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:21.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205357061.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27556
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.21
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.73
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.12
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.14
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.36
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.99
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.51
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.59
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.00
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.86
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.20
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.54
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.92
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.95
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908376
   j =  2                              :            45794
   j =  3                              :               12
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908480
   j =  2                              :            45754
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.97e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.10
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.58
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.60
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.56
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.31
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.09
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.82
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.87
 p-value of test no 133                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.10
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.16
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.28
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.66
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.55
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.18
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.82
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.16
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.39
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.14
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.15
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.66
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.66
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.22
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.97
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.01
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.80
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.83
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.73
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.32
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.64
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.04
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.22
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.85
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  265.86
 p-value of test no 170                :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.34
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.45
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5225.77
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.84
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.44
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.77
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.20
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.31
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    2.28
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.26
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.12
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.92
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.56
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.68
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.26
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.50
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.41
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.39
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.12
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.26
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11509.27
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.81
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999927695
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.92
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000055969
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 245                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 248                :    0.93
 
 Sample variance                       :   0.078
 p-value of test no 249                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:06.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206307333.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27557
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.75
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.13
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.08
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.72
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.61
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.80
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.96
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.38
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.47
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.49
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.40
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.53
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.58
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.86
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46203
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907597
   j =  2                              :            46197
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45251
 p-value of test no 71                 :    0.9983
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869251
   j =  1                              :        399909502
   j =  2                              :            45243
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.94
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.78
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.24
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.94
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.56
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.02
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.78
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.79
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.12
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.08
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.06
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.61
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.97
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.18
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.79
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.31
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.05
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.19
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.69
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.23
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.50
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.14
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.51
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.67
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.04
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.50
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.06
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.25
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.21
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.91
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.64
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.14
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.16
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.50
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.95
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.50
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.10
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.89
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.46
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.56
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.87
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.54
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.01
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.64
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.12
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.10
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.44
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.54
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.56
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999899927
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.59
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999994523
 
 Normal statistic for number of bits   :  -0.043
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:22.31
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207323141.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27558
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.21
 p-value of test no 22                 :  7.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.44
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.01
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.90
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.77
 p-value of test no 55                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.60
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.82
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.29
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.12
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.60
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.58
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907965
   j =  2                              :            46013
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908727
   j =  2                              :            45632
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.44
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.60
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.13
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.15
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.43
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.78
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.11
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.46
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.03
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.94
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.55
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.88
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.08
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.87
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.10
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.20
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.06
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.28
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.01
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.40
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.98
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.19
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.35
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.88
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.87
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.11
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.16
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.52
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.43
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.56
 p-value of test no 167                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.23
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.55
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.13
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.16
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.96
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.52
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.33
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.23
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.14
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 186                :  1.0e-3
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 187                :  5.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.72
 p-value of test no 188                :  3.2e-3
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.44
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.89
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.32
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.10
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.55
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4653.50
 p-value of test no 222                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.24
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.91
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4296.59
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.23
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.08
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.08
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000024178
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.44
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000041881
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 246                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 247                :  3.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.89
 p-value of test no 248                :  1.9e-3
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:08.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208273413.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27559
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.48
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.66
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   23.18
 p-value of test no 47                 :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.60
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.35
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.86
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.58
 p-value of test no 51                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.58
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.07
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.88
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.70
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.58
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.58
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.99
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.83
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.16
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.94
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.28
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908392
   j =  2                              :            45801
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908099
   j =  2                              :            45946
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9923
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.47
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.36
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.14
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.89
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.74
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.37
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.91
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.37
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.31
 p-value of test no 136                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.01
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17296.76
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.46
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.97
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.22
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.58
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.64
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.75
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.92
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    7.81
 p-value of test no 154                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.03
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.47
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.85
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.55
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.03
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.77
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.44
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.54
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.07
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.48
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.32
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.07
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.53
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.39
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.24
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.24
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.31
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4792.37
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  445.58
 p-value of test no 174                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.65
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.38
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.82
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.87
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.83
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.77
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.00
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.91
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.11
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.20
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.15
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.91
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.40
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000022345
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.87
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999943790
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:30.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209321989.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27560
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 8                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.89
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.93
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.55
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.29
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.24
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.45
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.19
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.37
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.76
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.50
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.09
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.11
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.83
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.10
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.02
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45602
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908801
   j =  2                              :            45592
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908375
   j =  2                              :            45808
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.67
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.34
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.36
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.70
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.09
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.03
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.92
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.11
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.18
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.63
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.31
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.57
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.93
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.99
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.45
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.53
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.86
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.95
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.36
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.32
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.49
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.19
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.57
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.65
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.48
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.89
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.00
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.27
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.06
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.91
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.70
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.60
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.82
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.73
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.83
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.93
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  465.53
 p-value of test no 174                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.01
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.21
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.79
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.99
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.80
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.63
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.02
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.65
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.31
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.24
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.49
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.94
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.77
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000074116
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.61
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000056527
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 243                :  8.1e-3
 
 Sample variance                       :    2.10
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:15.44
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189071366.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27561
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4546
 p-value of test no 14                 :  8.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    2.75
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.36
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.51
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.36
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.62
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.02
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.33
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.34
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.23
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.43
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.49
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5193.65
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907848
   j =  2                              :            46073
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45347
 p-value of test no 71                 :    0.9936
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869347
   j =  1                              :        399909311
   j =  2                              :            45337
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 93                 :  9.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 95                 :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9972
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-6
 p-value of test no 113                :    0.9969
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.32
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.99
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.79
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.40
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.46
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.13
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.32
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.60
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.57
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.91
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.83
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.91
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.54
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.77
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.69
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.60
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.18
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.51
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.54
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.72
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.09
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.87
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.50
 p-value of test no 161                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.65
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.24
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.82
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.28
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.03
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.27
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.91
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.34
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.33
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.17
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.17
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.26
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.89
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.43
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.50
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 204                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.07
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.23
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.88
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.53
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.21
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.98
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.73
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.23
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.52
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.34
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000141718
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.58
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999932945
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:59.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         8.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190119942.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27562
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     664
 p-value of test no 31                 :  5.3e-3
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.14
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.62
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.03
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.24
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.42
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.56
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.04
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.57
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7106.12
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.28
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.99
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.43
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.05
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.76
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908449
   j =  2                              :            45765
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908083
   j =  2                              :            45951
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.79
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.25
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.67
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.07
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.88
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.36
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.48
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.19
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.94
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.27
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.78
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.98
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.08
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.50
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.52
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.31
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.78
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.87
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.02
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.17
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.44
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.39
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.92
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.23
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.05
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.98
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.54
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.57
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.22
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.74
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.98
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.15
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.54
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.58
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.20
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.56
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.42
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.65
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.72
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 183                :    0.01
 
 Sample variance                       :    2.03
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.73
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 202                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.71
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.39
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.19
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.75
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.27
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.64
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.44
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.91
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.08
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.54
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.49
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000112975
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.67
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999922949
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 237                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.64
 p-value of test no 238                :  4.2e-3
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 247                :    0.9985
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:19:31.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191201286.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27563
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 17                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.11
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.93
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.45
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.60
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.87
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.66
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.62
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.72
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.74
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.53
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.04
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6865.62
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.23
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 63                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 64                 :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.90
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.71
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.26
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45442
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869442
   j =  1                              :        399909116
   j =  2                              :            45442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907692
   j =  2                              :            46148
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
 p-value of test no 107                :    0.9967
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.18
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.14
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.19
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.60
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.28
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.13
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.22
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.39
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.75
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.37
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.23
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17342.63
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.58
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.09
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.51
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.20
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.00
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.53
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.24
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.55
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.22
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.59
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.48
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.92
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.34
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.67
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.16
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.89
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.99
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.54
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.84
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5190.57
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.95
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.39
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.73
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.85
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.95
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.00
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.90
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.40
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.84
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.52
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.82
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.03
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.34
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.84
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.03
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.73
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.39
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.73
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000045412
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.95
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000116434
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:48.35
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192839686.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27564
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 9                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    5.43
 p-value of test no 26                 :  1.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.19
 p-value of test no 47                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.81
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.86
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.94
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.69
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.51
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.13
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.86
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.47
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.64
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.16
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.07
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.17
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.34
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908139
   j =  2                              :            45929
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907898
   j =  2                              :            46045
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.49
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.80
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.49
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.66
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.66
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.08
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.56
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.71
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.17
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17157.34
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.12
 p-value of test no 146                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.37
 p-value of test no 147                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.63
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.73
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.96
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.16
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.05
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.74
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.69
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.77
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.09
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.07
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.61
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.31
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.33
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.28
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.22
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.60
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.17
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.69
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.17
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.41
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.07
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.03
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.74
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.61
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.97
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :-1.40e-16
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 188                :    0.9904
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.41
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.79
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.19
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.49
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.63
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.21
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.95
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3900.19
 p-value of test no 227                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.78
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.21
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.11
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.24
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999954578
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.29
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000098638
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:22.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193724422.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27565
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7048
 p-value of test no 21                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    4.06
 p-value of test no 33                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.68
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.20
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.39
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.43
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.21
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.59
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.67
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.49
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.92
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.64
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.82
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.60
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46148
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870148
   j =  1                              :        399907707
   j =  2                              :            46142
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908028
   j =  2                              :            45983
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.59
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.20
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.72
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.67
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.10
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.37
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.84
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.50
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.84
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.45
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.63
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.08
 p-value of test no 146                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.89
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.21
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.51
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.98
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.33
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.24
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.73
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.91
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.11
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.93
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.19
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.43
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.63
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.75
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.75
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.56
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.70
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.97
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.76
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.78
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.93
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.42
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.78
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.66
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    2.30
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.57
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.22
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10280.22
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.93
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.05
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.81
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.44
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.87
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11557.53
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.95
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.69
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999982079
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.27
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000052900
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 235                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:41.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
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 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27566
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    3.00
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.18
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.29
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.46
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.67
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.46
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.62
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.57
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.08
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.00
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.90
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.23
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.05
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.37
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46250
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870250
   j =  1                              :        399907503
   j =  2                              :            46244
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908423
   j =  2                              :            45784
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.54
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.26
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.98
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.41
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.19
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.42
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.02
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.52
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.92
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 143                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    5.98
 p-value of test no 144                :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18046.99
 p-value of test no 145                :  5.4e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.38
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.64
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.55
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.06
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.91
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.65
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.34
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.94
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.03
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.77
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.79
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.14
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.80
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.14
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.02
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.86
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.78
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.17
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.90
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.40
 p-value of test no 166                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.09
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.08
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.49
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.15
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.26
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.98
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.89
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.18
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.78
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.23
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.55
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.53
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.24
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.97
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.27
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.74
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.80
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.69
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.44
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.70
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12157.71
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.69
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999778235
 
 Normal statistic for number of bits   :   -1.75
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.78
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000230572
 
 Normal statistic for number of bits   :    1.82
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:32.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  73  GCD                             5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195952646.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27567
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    4.59
 p-value of test no 42                 :  4.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.86
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.46
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.46
 p-value of test no 50                 :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.63
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.82
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.15
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.89
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.16
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.92
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.49
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.71
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.92
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907852
   j =  2                              :            46065
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908671
   j =  2                              :            45660
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 72                 :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.33
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.76
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.40
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.96
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.07
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.06
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.62
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.05
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.86
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17218.71
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.04
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.96
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.72
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.62
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.47
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.99
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.80
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.68
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.60
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.99
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.03
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.85
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.28
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.16
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.16
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.60
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.33
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.02
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.41
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.49
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.89
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.43
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.29
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.18
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.99
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.88
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.88
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.45
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.33
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.63
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9667.76
 p-value of test no 211                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.97
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.53
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4677.23
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.57
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.51
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.79
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.43
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.09
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999985370
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.29
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999921749
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 245                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:51.09
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197066758.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27568
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    4.02
 p-value of test no 27                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.87
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.91
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.75
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.27
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.12
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.57
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.04
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.21
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.79
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.82
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.18
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.34
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.79
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.15
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908072
   j =  2                              :            45958
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907996
   j =  2                              :            45996
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.71
 p-value of test no 119                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.44
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.85
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.04
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.26
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.83
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.90
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.41
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.60
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.95
 p-value of test no 146                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.81
 p-value of test no 147                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    7.89
 p-value of test no 148                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.09
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.13
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.42
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.86
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.63
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.04
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.36
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.74
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.72
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.21
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.84
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.03
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.10
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.94
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.51
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.55
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.20
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.25
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.48
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.09
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.74
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.42
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.27
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.96
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.36
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.53
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.04
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.35
 p-value of test no 179                :  9.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
 p-value of test no 180                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 186                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.08
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.86
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
 p-value of test no 205                : 1 -  7.6e-5    *****
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.31
 p-value of test no 207                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.29
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.63
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.16
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 224                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.12
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4364.64
 p-value of test no 227                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.23
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.65
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.31
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.30
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999849650
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.29
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999914588
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:09.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198213638.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27569
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    3.27
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.35
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.22
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.80
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.88
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.81
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.31
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.18
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.18
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.26
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.42
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.77
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.97
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.86
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.63
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.76
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.69
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908307
   j =  2                              :            45839
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908562
   j =  2                              :            45710
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.34e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.15
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.63
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.97
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.69
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.82
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.67
 p-value of test no 135                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.70
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17569.02
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.04
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.09
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.16
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.31
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.64
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.03
 p-value of test no 151                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.78
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.53
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.69
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.95
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.38
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.41
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.85
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.30
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.55
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.05
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.99
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.83
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.72
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.07
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.06
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.54
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.72
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.71
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.67
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.51
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.06
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.03
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.21
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.26
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.72
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.73
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.26
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.85
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.60
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.92
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.45
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.57
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.48
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11554.02
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.89
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.89
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000073288
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.76
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000067660
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 245                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.60
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199327750.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27570
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.93
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.44
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.27
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.00
 p-value of test no 51                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.88
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.58
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.41
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.65
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.57
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.17
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.15
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.63
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.55
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907958
   j =  2                              :            46015
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908009
   j =  2                              :            45988
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.23
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.01
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.96
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.05
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.18
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.36
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.84
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.01
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.54
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.05
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.12
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.46
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.26
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.94
 p-value of test no 149                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.34
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.43
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.32
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.96
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.12
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.04
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.86
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.99
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.28
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.51
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.04
 p-value of test no 161                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.08
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.33
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.91
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.19
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.76
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.07
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.45
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.31
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.28
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.09
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.64
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.09
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.20
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.07
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.07
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.34
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 209                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    5.27
 p-value of test no 210                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10416.41
 p-value of test no 211                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-4
 p-value of test no 212                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10313.36
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.52
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.41
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.19
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.59
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.69
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11552.34
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.86
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999968807
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.34
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999921812
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:09.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200376326.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27571
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    6.07
 p-value of test no 27                 :  9.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.75
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.30
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.24
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.33
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.37
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.97
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.00
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.17
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.75
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.36
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.83
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.66
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.48
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.52
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908273
   j =  2                              :            45859
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908261
   j =  2                              :            45862
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-6
 p-value of test no 109                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 3.98e-4
 p-value of test no 110                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 111                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.18
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.49
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.13
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.68
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.74
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.03
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.93
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.22
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17488.44
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.37
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.93
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.25
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.86
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.38
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.62
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.13
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.84
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.83
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.65
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.98
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.58
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.42
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.87
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.41
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.07
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.73
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.42
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.74
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.63
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.35
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.25
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.12
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.27
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.38
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  477.00
 p-value of test no 172                :  8.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.93
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.68
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.21
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.29
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.74
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.47
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.03
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9788.47
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 216                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.41
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.71
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.19
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.81
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12081.64
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.31
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.35
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999810578
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.78
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999982547
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.047
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:06.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2S, t = 3         9.2e-4
  79  RandomWalk1 M (L=10000, r=15)   8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201424902.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27572
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 11                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 18                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9943
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.45
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.50
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.69
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.72
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.88
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.16
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.59
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.88
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6874.92
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.98
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.09
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.95
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.61
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907762
   j =  2                              :            46110
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908222
   j =  2                              :            45883
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 116                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.56
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.52
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.14
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.79
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.70
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.22
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.82
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.47
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.33
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.67
 p-value of test no 135                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.84
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.30
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.36
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.35
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.58
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.35
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.25
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.89
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.93
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.11
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.98
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.89
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.69
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.70
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.97
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.05
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.68
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.10
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.85
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.02
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.03
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  298.20
 p-value of test no 169                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.38
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.01
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.89
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.83
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.02
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.85
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.30
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.88
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.69
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.68
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.29
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 221                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.87
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.75
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.35
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.19
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.01
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.18
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.32
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999853820
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.30
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999928847
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.058
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 R (L=10000, r=0)    0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202440710.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27573
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 10                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5288
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.62
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.63
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.91
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.01
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.64
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.42
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.63
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.65
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.52
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.58
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.53
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.96
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.10
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.23
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.86
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5117.50
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907740
   j =  2                              :            46127
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908645
   j =  2                              :            45673
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.80
 p-value of test no 119                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.82
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  109.19
 p-value of test no 121                :  8.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.54
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.82
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.42
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.03
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.01
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.92
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.04
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.07
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.21
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.71
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.20
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.15
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.93
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.54
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.48
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.90
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.70
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.37
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.87
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.48
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.52
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.03
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.71
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.18
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.74
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.84
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.73
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  450.74
 p-value of test no 169                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.26
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.17
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.28
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.47
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.52
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.60
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.02
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    2.07
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-3
 p-value of test no 185                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.24
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.96
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.65
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.96
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.63
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.91
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.30
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.15
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.34
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.21
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.32
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000102517
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000030535
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:02.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  61  WeightDistrib, r = 28           8.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203423750.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27574
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.31
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.31
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.88
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.31
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.65
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.12
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.01
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.28
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.32
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1310.63
 p-value of test no 56                 :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.59
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.40
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.18
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.62
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.19
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.32
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46254
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870254
   j =  1                              :        399907495
   j =  2                              :            46248
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907792
   j =  2                              :            46098
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.14
 p-value of test no 116                :  8.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.81
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.15
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.14
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.99
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.56
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.26
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.28
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17172.72
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.51
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.46
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.82
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.98
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.11
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.31
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.03
 p-value of test no 153                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.15
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.18
 p-value of test no 155                :  8.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.27
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.96
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.28
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.82
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.03
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.76
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.71
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.37
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.54
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.15
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.71
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.44
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.15
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.12
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.37
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.95
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.73
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.40
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.61
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.26
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.06
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.84
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.70
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.94
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.34
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.74
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.34
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.78
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.01
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.07
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.27
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.68
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999984389
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.85
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000008431
 
 Normal statistic for number of bits   :   0.067
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:06.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               8.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204570630.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27575
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    2.97
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.54
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.54
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.41
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.63
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.57
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.32
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.53
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.52
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.22
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.40
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.31
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.10
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.68
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.98
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.66
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908214
   j =  2                              :            45893
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907923
   j =  2                              :            46037
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.32
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.21
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.58
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.72
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.09
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.00
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.44
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.61
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.59
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17166.48
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.19
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.48
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.73
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.15
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.35
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.95
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.27
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.43
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.91
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.87
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.66
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.29
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.44
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.08
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.16
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.28
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.64
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.55
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.12
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.43
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.38
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.41
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.72
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.95
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.56
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.99
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.32
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.71
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.78
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.41
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.51
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.85
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.47
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.77
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.71
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.51
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.45
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11543.52
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.83
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999929738
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.64
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999840344
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.97
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205619206.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27576
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 5                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.17
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.78
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.11
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.70
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.69
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.23
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.24
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.79
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.21
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.23
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.93
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.34
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.31
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.35
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.41
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46463
 p-value of test no 70                 :  3.3e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870463
   j =  1                              :        399907077
   j =  2                              :            46457
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907542
   j =  2                              :            46220
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-5
 p-value of test no 113                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.54
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.54
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.82
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.14
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.24
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.86
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.34
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.41
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.79
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.89
 p-value of test no 136                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.70
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.65
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.96
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.49
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.24
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.59
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.21
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.05
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.46
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.01
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   39.89
 p-value of test no 155                :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.63
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.82
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.32
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.06
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.42
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.82
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.94
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.49
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.26
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.86
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.96
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.87
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.83
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.52
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.88
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.38
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.31
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.10
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.94
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.15
 p-value of test no 184                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.16
 p-value of test no 189                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.05
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.42
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.41
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.81
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.96
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.98
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.99
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.74
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.77
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.62
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.85
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000099232
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.45
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000084739
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:32.09
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206667782.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27577
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.73
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.69
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.96
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.84
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.62
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.29
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.06
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.27
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.39
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.25
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.61
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.73
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.59
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.78
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.11
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908551
   j =  2                              :            45717
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908174
   j =  2                              :            45910
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.54
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.37
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.13
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.11
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.53
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.90
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.68
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.03
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17683.98
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.87
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.01
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.62
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.46
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.45
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.20
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.20
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.10
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.95
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.26
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.73
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.61
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.02
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.76
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.07
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.06
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.92
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.11
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.01
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.33
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.65
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.41
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.69
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.67
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.86
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.60
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.76
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.11
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.69
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.31
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.15
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.20
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10291.68
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.17
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.09
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.74
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.03
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.56
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.65
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.04
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.36
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999988310
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.08
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000114958
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 238                :    0.46
 
 Sample variance                       :    2.36
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 245                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 246                :  2.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.88
 p-value of test no 247                :  1.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.16
 p-value of test no 248                :  7.8e-4    *****
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:09.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  105  AutoCor, d=1, r=27              7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207716358.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27578
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 7                  :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.03
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.17
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.90
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.52
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.46
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.64
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.15
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.82
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.93
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.99
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.75
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.89
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.16
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.46
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908201
   j =  2                              :            45889
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908896
   j =  2                              :            45546
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.06
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.49
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.41
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.64
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.10
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.64
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.92
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.92
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17491.75
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.30
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.66
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.22
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.11
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.93
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.47
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.92
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.07
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.18
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.40
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.62
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.82
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.22
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.54
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.41
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.91
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.34
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.55
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.12
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.96
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.75
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.32
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.66
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.88
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.60
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.79
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.84
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.53
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.66
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.95
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.03
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.44
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.47
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.53
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.20
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.81
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.97
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.72
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.36
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.45
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.96
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.14
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000126280
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.52
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999748793
 
 Normal statistic for number of bits   :   -1.99
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:51.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208764934.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27579
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.16
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.54
 p-value of test no 46                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.57
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.92
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.46
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.95
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.55
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.05
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.26
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.87
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.74
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.82
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.98
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.32
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.43
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908823
   j =  2                              :            45578
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908274
   j =  2                              :            45860
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.90
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.27
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.38
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.75
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.56
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.39
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-4
 p-value of test no 131                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.50
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.55
 p-value of test no 134                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.66
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.73
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17338.82
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.33
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.16
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.67
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.29
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.36
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.56
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.31
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.22
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.59
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.50
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.28
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.05
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.94
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.00
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.33
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.30
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  404.04
 p-value of test no 163                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.86
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.69
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.72
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.32
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.94
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  487.66
 p-value of test no 169                :  1.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.99
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.69
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.30
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.52
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.71
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.04
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.51
 p-value of test no 178                :    0.9907
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.85
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.52
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.14
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.29
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.34
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.96
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.39
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.83
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.25
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.01
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.81
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.39
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.80
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000044230
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.08
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999977927
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    3.16
 p-value of test no 249                :  8.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:58:55.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                0.9993 
  77  RandomWalk1 J (L=1000, r=20)    0.9994 
  78  RandomWalk1 R (L=10000, r=0)    1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209813510.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27580
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 11                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.35
 p-value of test no 23                 :  6.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    3.98
 p-value of test no 27                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.89
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.35
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.66
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.75
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.29
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.20
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.31
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.61
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7085.54
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-3
 p-value of test no 58                 :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.26
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.31
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.52
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.31
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.65
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46512
 p-value of test no 70                 :  1.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870512
   j =  1                              :        399906980
   j =  2                              :            46504
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908508
   j =  2                              :            45740
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.82
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.59
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.69
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.81
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.94
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 140                :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.15
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17629.31
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.41
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.31
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.63
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   39.15
 p-value of test no 150                :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.57
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.25
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.64
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.41
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.84
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.87
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.97
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.82
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.04
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.89
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.35
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.97
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.38
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.59
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.31
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.00
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.92
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.72
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.79
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.18
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.86
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.74
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.01
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.38
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.29
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.49
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.73
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.99
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.18
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9773.25
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.32
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.78
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.19
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.71
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.50
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.38
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.45
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999815366
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.45
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000086806
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 245                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.086
 p-value of test no 253                :    0.53
 
 Sample variance                       :    2.10
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:51.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189104135.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27581
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 12                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7548
 p-value of test no 19                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.17
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.77
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.83
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.34
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.35
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.09
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.40
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.57
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.89
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.77
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.50
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.25
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.59
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.73
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4869.55
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908344
   j =  2                              :            45819
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907867
   j =  2                              :            46062
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.94
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.95
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.59
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.28
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.11
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.36
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.78
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.22
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.61
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.46
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.74
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.05
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.07
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.60
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.05
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.01
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.18
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.37
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.46
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.90
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.43
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.27
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.61
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.51
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.12
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.81
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.70
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.17
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.09
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.19
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.94
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.21
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.15
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.57
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.22
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.20
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.30
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.36
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.33
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.39
 p-value of test no 178                :    0.9921
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.04
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.77
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.55
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.74
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.55
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.93
 p-value of test no 216                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.19
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.05
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.36
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.87
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.06
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11481.17
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.45
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000150031
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.72
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999954284
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 251                :  2.0e-4    *****
 
 Anderson-Darling statistic = A2       :    5.35
 p-value of test no 252                :  2.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.86
 p-value of test no 253                :  2.1e-3
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:34.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190316574.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27582
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9924
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.07
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.42
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.85
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.45
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.35
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.26
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.11
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.23
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.19
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.54
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.01
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.40
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.44
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908682
   j =  2                              :            45656
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908236
   j =  2                              :            45879
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 99                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.36
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.90
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.01
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.04
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.91
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.11
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.60
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.62
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.83
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.06
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.09
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.14
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.80
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.87
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.20
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.49
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.57
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.66
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.51
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.71
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.27
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.75
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.52
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.34
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.39
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.20
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.07
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.46
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.83
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.31
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.62
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.77
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.23
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.60
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.15
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.56
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.76
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.66
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.94
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.40
 p-value of test no 179                :    0.9918
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.25
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.20
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.80
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.84
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.02
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.23
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.59
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.15
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.55
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.98
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.99
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.52
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999831713
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.45
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999964802
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:13.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191692830.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27583
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 3                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9943
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.16
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    4.46
 p-value of test no 36                 :  5.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     341
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    4.80
 p-value of test no 38                 :  3.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.12
 p-value of test no 42                 :    0.9997    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.15
 p-value of test no 47                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.12
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.91
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.70
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.11
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.20
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.02
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.06
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.93
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.89
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.61
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.75
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.72
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908144
   j =  2                              :            45925
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907982
   j =  2                              :            46003
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.12
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.81
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.82
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.35
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.82
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.16
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.04
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.90
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.77
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.91
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.81
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.45
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.10
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.53
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.22
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.22
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.01
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.75
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.17
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.83
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.19
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.47
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.46
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.32
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.94
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.34
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.90
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.30
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.73
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.48
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.13
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.36
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.63
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.80
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.99
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.74
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.20
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.98
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.69
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.93
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.56
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.33
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.66
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.54
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.05
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.83
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.59
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 209                :    0.9931
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9759.13
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.43
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.44e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.40
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.84
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.70
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.79
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.71
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.08
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.50
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000029944
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.66
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000039796
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:59.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192643102.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27584
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.48
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.51
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.65
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.49
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.70
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.07
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.18
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6805.56
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.11
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.98
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.30
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.84
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.89
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908057
   j =  2                              :            45967
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908654
   j =  2                              :            45664
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  8.4e-3
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.14
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.78
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.96
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.05
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.22
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.31
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.11
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.77
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.07
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.68
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.92
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.33
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.33
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.64
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.66
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.16
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.66
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.59
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.15
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.09
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.14
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.48
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.56
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.95
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.77
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.47
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.25
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.99
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.74
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.67
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.13
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.27
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.89
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.96
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.91
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.98
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.63
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.50
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.63
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.98
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.37
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.94
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.32
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.83
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.34
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11482.25
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12150.75
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000003619
 
 Normal statistic for number of bits   :   0.029
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.39
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999963629
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:12.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193527838.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27585
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.63
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    3.48
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.44
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.79
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.97
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.99
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.47
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.89
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.10
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.59
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.40
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.40
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.44
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908197
   j =  2                              :            45897
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45569
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908863
   j =  2                              :            45567
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.58
 p-value of test no 118                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.76
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.64
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.17
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.66
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.82
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.84
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.20
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.35
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.62
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.46
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.24
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.08
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.36
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.66
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.32
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.06
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.49
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.92
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.66
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.53
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.00
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.50
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.66
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.82
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.88
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.70
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.14
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.72
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.45
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.37
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.11
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.68
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.31
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.44
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.88
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.86
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.18
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.47
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.80
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.22
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.68
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.47
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 209                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 210                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10366.38
 p-value of test no 211                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.41
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.11
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.85
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.57
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.62
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.37
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.63
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.14
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999969938
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.22
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000005071
 
 Normal statistic for number of bits   :   0.040
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.066
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:17.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194412574.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27586
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7491
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     187
 p-value of test no 43                 :  2.0e-3
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.43
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.13
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.47
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.30
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.48
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.20
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.74
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.06
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.92
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.52
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.92
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.62
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.22
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907984
   j =  2                              :            46005
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908018
   j =  2                              :            45988
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 115                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.56
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.51
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.04
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.03
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.05
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.31
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.84
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.51
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.48
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.13
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17171.77
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.07
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.35
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.90
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.88
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.54
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.24
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.53
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.73
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.82
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.32
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.50
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.09
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.75
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.09
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.01
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.07
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.98
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.81
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.03
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4819.10
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.99
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.22
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.39
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.08
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.78
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.17
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.06
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.41
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.57
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.27
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
 p-value of test no 201                :    0.9989
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.94
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.50
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9772.82
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.54
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.86
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 224                :    0.9909
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 225                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4618.39
 p-value of test no 226                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.07
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.94
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.33
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.40
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.35
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000118447
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.94
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000013741
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:24.80
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195756062.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27587
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4199
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.69
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.99
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.79
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.18
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.08
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.86
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.14
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.11
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.35
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.81
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.10
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.79
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.27
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.49
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.31
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907677
   j =  2                              :            46160
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908883
   j =  2                              :            45554
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.96
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.19
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.16
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.15
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.73
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.06
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.13
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.72
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17746.20
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.96
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.36
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.78
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.66
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.81
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.20
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.05
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.55
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.81
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.17
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.46
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.23
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.38
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.57
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.03
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.54
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.20
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.66
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.66
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.78
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.88
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.90
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.94
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.68
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.52
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.93
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.44
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.81
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.94
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.89
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.05
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.25
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.90
 p-value of test no 217                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.08
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.47
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.10
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.19
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.25
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.14
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.33
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000087469
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.77
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000018997
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:22.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196608030.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27588
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 10                 :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.24
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.88
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.50
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.18
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.07
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.51
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.41
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.95
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1521.59
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6858.74
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.54
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.70
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.38
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4948.67
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908086
   j =  2                              :            45954
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908057
   j =  2                              :            45970
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.96
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.73
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.03
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.69
 p-value of test no 123                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.96
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.79
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.39
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.69
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.95
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.86
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.91
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.06
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.37
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.35
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.38
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.66
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.33
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.71
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.79
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.28
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.08
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.40
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.05
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.29
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.45
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.40
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.03
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.18
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.83
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.50
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.87
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.77
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.13
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.58
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.63
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.09
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.05
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.79
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-3
 p-value of test no 186                :    0.9987
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.93
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.39
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.08
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.32
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.11
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.00
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.37
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.30
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.06
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.78
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.99
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999849659
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.47
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000058435
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9961
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:48.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197558302.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27589
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 9                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    3.87
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.47
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.50
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.47
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.01
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.52
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.91
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.49
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.66
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.92
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.29
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.55
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.41
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.33
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.42
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.33
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.12
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907754
   j =  2                              :            46117
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908206
   j =  2                              :            45891
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 87                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 98                 :    0.9915
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 99                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.77
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.70
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.33
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.28
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.94
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 126                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.95
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.36
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.97
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.48
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.34
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.34
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.84
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.36
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.64
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.19
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.23
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.56
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.26
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.41
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.45
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.20
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.43
 p-value of test no 162                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.00
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.36
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.06
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.07
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.81
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.62
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.85
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.54
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.21
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.16
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.54
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.16
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.73
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.73
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    2.05
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.27
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.49
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.94
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.71
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.89
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.45
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5074.40
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.27
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.46
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.03
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.30
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.48
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000102547
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.52
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000113233
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 236                :    0.9935
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:41.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198836254.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27590
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 5                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.12
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.28
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.20
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.87
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.68
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.99
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.91
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.20
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.24
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.18
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.31
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.35
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907750
   j =  2                              :            46119
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908353
   j =  2                              :            45822
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.68
 p-value of test no 117                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.83
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.50
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.66
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.24
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.21
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.88
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.35
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17216.57
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.93
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.28
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.81
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.00
 p-value of test no 149                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.08
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.42
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.24
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.67
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.34
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.56
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.20
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.19
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.30
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.66
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.69
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.85
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.28
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.68
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.36
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.60
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.38
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  315.78
 p-value of test no 169                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.12
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.01
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.54
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.95
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.70
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.97
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.34
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.94
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.57
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.73
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.82
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.44
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.45
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.07
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.35
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.27
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.22
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.24
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.20
 p-value of test no 231                :  9.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000068407
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.74
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000024433
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:03.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200081438.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27591
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9916
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.25
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.02
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.26
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.16
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.71
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.11
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.29
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.59
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.48
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.87
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45681
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869681
   j =  1                              :        399908640
   j =  2                              :            45677
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907987
   j =  2                              :            45999
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.36
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.95
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.39
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.82
 p-value of test no 123                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.58
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.47
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.04
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.28
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.35
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.24
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.81
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.74
 p-value of test no 147                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.83
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.88
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.93
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.26
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.97
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.66
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.13
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.79
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.84
 p-value of test no 158                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.29
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.08
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.83
 p-value of test no 161                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.82
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.20
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.87
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.79
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.95
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.29
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.30
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.52
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.97
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.75
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4769.80
 p-value of test no 173                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.43
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.91
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.91
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.79
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.77
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.09
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.66
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.55
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.06
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.10
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4321.84
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.88
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11598.57
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.53
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.94
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999979253
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.71
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999932312
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:00.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200966174.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27592
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997311
   j =  2                              :             1343
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 12                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.61
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.54
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.25
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.92
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.46
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.74
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.69
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.42
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.90
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.14
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.13
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.55
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.64
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.33
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908267
   j =  2                              :            45862
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908384
   j =  2                              :            45805
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.55
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.15
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.87
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.36
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.40
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.71
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.79
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.80
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.91
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.15
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17736.60
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.10
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.29
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.78
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.06
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.28
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.76
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.22
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.14
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.82
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.21
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.84
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.33
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.52
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.85
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.41
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.13
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.00
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.80
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.07
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.20
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.84
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.02
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.01
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.02
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.11
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.89
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.25
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.46
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 181                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 183                :  7.9e-3
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.45
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.33
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.44
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.10
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.37
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.50
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.38
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.84
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.68
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.29
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.58
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999986087
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.12
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000097504
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:59.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202276894.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27593
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4536
 p-value of test no 17                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    3.53
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.99
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.39
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.88
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.61
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.20
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.83
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.12
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.95
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.22
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.33
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.32
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.49
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.20
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.47
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908230
   j =  2                              :            45879
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908178
   j =  2                              :            45911
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 98                 :  5.2e-4    *****
 
 Anderson-Darling statistic = A2       :    5.68
 p-value of test no 99                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.82
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.24
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.95
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   70.08
 p-value of test no 123                :  8.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.87
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.65
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 126                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 128                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   68.56
 p-value of test no 129                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.63
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.62
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.39
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17579.91
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.13
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.76
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.91
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.95
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.66
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.42
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.72
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.03
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.07
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.93
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.74
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.09
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.30
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.71
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.14
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.89
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.17
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.55
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.69
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.35
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.68
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.41
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.46
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.09
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.04
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.16
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.57
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.70
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.93
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.37
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.53
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.59
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.30
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.11
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.14
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.26
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.19
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.02
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.73
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11496.30
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.99
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.79
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000042028
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.97
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000020782
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:31.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           8.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203522078.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27594
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.35
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.80
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.81
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   90.70
 p-value of test no 52                 :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.57
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.00
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.43
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.97
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.39
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.58
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.97
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.23
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.03
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.27
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908101
   j =  2                              :            45945
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907981
   j =  2                              :            46008
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  4.1e-3
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.51
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.29
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.12
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.25
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.22
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.05
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.72
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.57
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.91
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.53
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17687.63
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.28
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.46
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.24
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.94
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.86
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.94
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.33
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.72
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.13
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.23
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.11
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.92
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.45
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.29
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.11
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.64
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.05
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.29
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.30
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.49
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.18
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.08
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.33
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.91
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.40
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.53
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.07
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.90
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.64
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.47
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.17
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.06
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.88
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.66
 p-value of test no 217                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.68
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.02
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.28
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.08
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.42
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.96
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.33
 p-value of test no 231                :  7.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999989909
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.61
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000081325
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    5.15
 p-value of test no 242                :  2.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.95
 p-value of test no 243                :  1.6e-3
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:31.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204537886.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27595
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.62
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    3.36
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.48
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.35
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.60
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.78
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.92
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.46
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.98
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.18
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.59
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6869.80
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.07
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.61
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.89
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.84
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908852
   j =  2                              :            45568
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908241
   j =  2                              :            45872
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.60
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.00
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   14.52
 p-value of test no 122                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.87
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.16
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.79
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.11
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.68
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.69
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.18
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.89
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.72
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.66
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.22
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.94
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.16
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.00
 p-value of test no 154                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.95
 p-value of test no 155                :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.99
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.02
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.43
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.61
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.58
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.40
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.88
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.54
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.21
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.59
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.38
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.89
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.75
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.32
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.96
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.65
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.29
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.61
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.85
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.74
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 188                :    0.96
 
 Sample variance                       :    2.21
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.31
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 199                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.46
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.33
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.57
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.88
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.76
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.04
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.52
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.69
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.57
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.95
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.23
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000065101
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.07
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000151714
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 236                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.99
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:30.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            0.9997 
  75  RandomWalk1 R (L=50, r=25)      0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205553694.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27596
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 12                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.29
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.03
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.83
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.93
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.39
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.84
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.16
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.77
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.84
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.53
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.83
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.50
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.49
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.02
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908407
   j =  2                              :            45789
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908309
   j =  2                              :            45844
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.53
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.44
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.43
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.42
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.38
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.29
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.15
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 131                :    0.9945
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.47
 p-value of test no 133                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 140                :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.98
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.95
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.58
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.15
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.69
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.87
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.10
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.86
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.55
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.86
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.86
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.18
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.04
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.37
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.38
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.59
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.31
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.03
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.47
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.43
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.91
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.05
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.10
 p-value of test no 169                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.93
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.52
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.34
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.95
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.59
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.00
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.74
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.06
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.06
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.03
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.23
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.46
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.50
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.62
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.24
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.44
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.50
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999923678
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.60
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000146920
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    2.14
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.06e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:26.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206503966.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27597
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9967
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.74
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.22
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.09
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.62
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.06
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.95
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.18
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.22
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.00
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.87
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.09
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.14
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.71
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.67
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.04
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908232
   j =  2                              :            45884
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.18
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.58
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.00
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.28
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.46
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.58
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.88
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.25
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.61
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.29
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17591.64
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.15
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.86
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.35
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.46
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.33
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.00
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.45
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.26
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.67
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.67
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.60
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.28
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.60
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.43
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.00
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.99
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.81
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.44
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.14
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.46
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.50
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.56
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.31
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.23
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.32
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.75
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.61
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.64
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.53
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.58
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.83
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.09
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.71
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.77
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.69
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.30
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.08
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.25
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3955.61
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11573.46
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.86
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.24
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000002992
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.97
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000128980
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:19.48
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207487006.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27598
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4158
 p-value of test no 17                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.81
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.12
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.03
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.70
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.27
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.94
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.20
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.41
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.51
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.84
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.67
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.79
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.64
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45489
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869489
   j =  1                              :        399909028
   j =  2                              :            45477
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908542
   j =  2                              :            45729
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9916
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    4.10
 p-value of test no 85                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 105                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.14
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.28
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.80
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.69
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.55
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.31
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.83
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.42
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.17
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17660.81
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.57
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.94
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.03
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.99
 p-value of test no 149                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.83
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.99
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.63
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.88
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.41
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.59
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.52
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.02
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.26
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.24
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.59
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.58
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.68
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.82
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.72
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.89
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.86
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.30
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.32
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.43
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.72
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.67
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.59
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.78
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 186                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.24
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.78
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.23
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.32
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.61
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.53
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.37
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.88
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.93
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.45
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.46
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000014647
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.35
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000119110
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.51
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208502814.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27599
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    3.18
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.73
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.04
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.59
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.57
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.42
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7210.14
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.23
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.23
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.43
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.00
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.27
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908104
   j =  2                              :            45945
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908153
   j =  2                              :            45916
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.16
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.09
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.35
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.55
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.36
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.44
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.35
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.44
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.53
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.73
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17341.82
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.13
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.83
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.86
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.23
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.97
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.27
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.91
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.22
 p-value of test no 155                :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.22
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.87
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.36
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.80
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.20
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.02
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.25
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.56
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.57
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.35
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.05
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.59
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.85
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.90
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.45
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.26
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.64
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.72
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.10
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.91
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.29
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.38
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.98
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.30
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.10
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.26
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.61
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.12
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.69
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.62
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.35
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11413.99
 p-value of test no 230                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.99
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999879722
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.82
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000055744
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.73
 
 Sample variance                       :    2.91
 p-value of test no 254                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:59:58.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209551390.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27600
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.44
 p-value of test no 35                 :  5.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9905
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.59
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.28
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.90
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.08
 p-value of test no 52                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.76
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.48
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1358.49
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.15
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.82
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.6e-3
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 64                 :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.03
 p-value of test no 65                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.99
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.37
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908229
   j =  2                              :            45878
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908260
   j =  2                              :            45867
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 101                :    0.9943
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.19
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.86
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.20
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.44
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.35
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.97
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.22
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.47
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17675.21
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.32
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.67
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.31
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.36
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.70
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.00
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.92
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.71
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.03
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.33
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.14
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.41
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.73
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.28
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.18
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.71
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.32
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.95
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.12
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.63
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.97
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.24
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.04
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.98
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.85
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.41
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.81
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.70
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.29
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.57
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.59
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.13
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.85
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.71
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.92
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.28
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.07
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.88
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.24
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.10
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.84
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.45
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000071551
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.90
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000046852
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -4.36e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.96
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:25:07.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189136904.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27601
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5567
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.45
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.96
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.12
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.78
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.66
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.11
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.42
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.66
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.30
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.26
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.83
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.46
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.31
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.91
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.98
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907966
   j =  2                              :            46008
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45492
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869492
   j =  1                              :        399909022
   j =  2                              :            45480
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.47
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.10
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.63
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.62
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.95
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.46
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.04
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17259.40
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.17
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.69
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.26
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.07
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.26
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.42
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.50
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.52
 p-value of test no 153                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.09
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.17
 p-value of test no 155                :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.51
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.48
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.62
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.99
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.03
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.82
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.56
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.08
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.19
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.00
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.15
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.16
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.06
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.93
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.27
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.53
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.36
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.88
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.44
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.28
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.89
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.36
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    2.11
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 193                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.04
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.92
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10238.10
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.18
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.59
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.56
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4269.39
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.56
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.73
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.13
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.56
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000073405
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.59
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999867317
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.037
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:54.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190840840.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27602
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 11                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.20
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.36
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.70
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.88
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.61
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.19
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.44
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.05
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.97
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.19
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.30
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.27
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5216.35
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907915
   j =  2                              :            46029
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908231
   j =  2                              :            45877
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 94                 :    0.9930
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9945
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.89
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.75
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.46
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.59
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.52
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.02
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.42
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.23
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.93
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.71
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17643.70
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.63
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.70
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.68
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.36
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.80
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.76
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.04
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.18
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.22
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.90
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.45
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.37
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.75
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.16
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.09
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.90
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.50
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.62
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.18
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.95
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.95
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.77
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.99
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.19
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.80
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.99
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.05
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.93
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.98
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.52
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.19
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.091
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.91
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.10
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.86
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.99
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.46
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.85
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.96
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.65
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.77
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.24
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.65
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.67
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999904319
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.87
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000085273
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:36.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191889416.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27603
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 9                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.77
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.65
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.47
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.94
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.48
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.76
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.70
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.02
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6887.34
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 58                 :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.90
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.46
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.39
 p-value of test no 66                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.31
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.13
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907842
   j =  2                              :            46076
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46179
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870179
   j =  1                              :        399907647
   j =  2                              :            46169
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.05
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.43
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.92
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.36
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.52
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.48
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.61
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.25
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.72
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17443.15
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.18
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.49
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.70
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.23
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.44
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.08
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.40
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.33
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.46
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.87
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.33
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.95
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.05
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.66
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.87
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.04
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.88
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.81
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.97
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.94
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.28
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.40
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.73
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.84
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.10
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.75
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.08
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.66
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.03
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.29
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.81
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.21
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.30
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.88
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.94
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.22
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.66
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.61
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.55
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.84
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.95
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999951467
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.13
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000056950
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192970760.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27604
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.47
 p-value of test no 35                 :  1.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.79
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.59
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.76
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.91
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.62
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.98
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.78
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.78
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.74
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.84
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.54
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1519.12
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.24
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.76
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.29
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.97
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.83
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5174.58
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908025
   j =  2                              :            45980
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908392
   j =  2                              :            45801
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 115                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.01
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.83
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.70
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.63
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.41
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.41
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.64
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.62
 p-value of test no 136                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.82
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17338.08
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.45
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.78
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.07
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.65
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.85
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.06
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.36
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.03
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.86
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.33
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.12
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.20
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.13
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.71
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.53
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.80
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.51
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.98
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.69
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.83
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.46
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.03
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.53
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.46
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.87
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.69
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.84
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.53
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.92
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.06
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.07
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.55
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.97
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.34
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.25
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.33
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.010
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.22
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.36
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.79
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.13
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.72
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.78
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.59
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000076753
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.30
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000085186
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:47.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193953800.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27605
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 6                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.22
 p-value of test no 46                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.86
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.48
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.60
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.96
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.73
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.82
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.42
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.46
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.02
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.66
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.86
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.23
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.21
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.07
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45519
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908967
   j =  2                              :            45509
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907753
   j =  2                              :            46113
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.67
 p-value of test no 117                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.44
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.10
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.00
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.59
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.15
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.41
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.37
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.13
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.37
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.54
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.81
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.81
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.11
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.66
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.95
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.88
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.55
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.64
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.07
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.63
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.06
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.89
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.39
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.23
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.88
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.59
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.23
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.89
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.63
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.01
 p-value of test no 166                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.60
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.46
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.28
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.38
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.90
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.31
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4784.17
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.98
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.60
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.41
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.23
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.76
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.31
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.18
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.11
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.18
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.08
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.60
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.88
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.46
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.64
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.93
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000061609
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.28
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000053626
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:22.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194969608.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27606
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.66
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.66
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.85
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.77
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.66
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.47
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.94
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.18
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.46
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.43
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.75
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.88
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.73
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908345
   j =  2                              :            45817
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907658
   j =  2                              :            46168
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9931
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-6
 p-value of test no 109                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.29
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.47
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.94
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.57
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.36
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.38
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.82
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.77
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.54
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.14
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17151.54
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.87
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.91
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.43
 p-value of test no 149                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.17
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.11
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.10
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.25
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.35
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.73
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.14
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.31
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.13
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.56
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.97
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.57
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.35
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.90
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.78
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.73
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.55
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.00
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.22
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.92
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.13
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.17
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.80
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.77
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.32
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.66
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.15
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 210                :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.27
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.46
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.39
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.25
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.16
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.52
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.46
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.64
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.45
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000117310
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.68
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000149890
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    4.86
 p-value of test no 242                :  3.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.81
 p-value of test no 243                :  2.5e-3
 
 Sample variance                       :    2.20
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:56.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196149256.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27607
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997319
   j =  2                              :             1339
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 11                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.71
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.49
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.85
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.29
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.74
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.22
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.09
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.68
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.47
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.11
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.59
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.16
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.72
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908365
   j =  2                              :            45813
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908076
   j =  2                              :            45959
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.95
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.57
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.73
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.95
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.79
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.18
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.78
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.35
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.39
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.23
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.93
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17645.77
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.59
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.84
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.02
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.20
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.32
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.71
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.43
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.61
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.45
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.65
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.27
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.05
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.51
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.47
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.08
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.45
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.05
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.13
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.57
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.02
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.54
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.01
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.22
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.46
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.15
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.66
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.76
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.24
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.06
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.27
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.89
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.28
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.36
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.27
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.29
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.94
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.25
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.47
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999929024
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.78
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000010771
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:23.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197165064.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27608
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 6                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7497
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.74
 p-value of test no 35                 :  1.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    5.86
 p-value of test no 36                 :  1.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.65
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.39
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.69
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.50
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.76
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.10
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.16
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.83
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.48
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7306.52
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.74
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.18
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.15
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.29
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908356
   j =  2                              :            45819
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908434
   j =  2                              :            45780
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 6.08e-4
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.90
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.93
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.43
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.99
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.00
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.60
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.66
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.34
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17554.82
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.27
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.00
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.71
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.88
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.66
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.21
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.06
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.28
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.70
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.72
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.03
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.78
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.23
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.86
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.81
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.02
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.38
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.11
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.95
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.05
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.13
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.64
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.09
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.70
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.83
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5184.84
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.19
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.73
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.00
 p-value of test no 176                :  3.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.67
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.88
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.13
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.43
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.89
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.44
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.07
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 219                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.35
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.75
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3934.79
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.59
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.69
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.71
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.43
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999847829
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.48
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999979877
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 246                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 247                :  4.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.57
 p-value of test no 248                :  5.1e-3
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:32.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198148104.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27609
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    3.78
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.93
 p-value of test no 35                 :  1.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.80
 p-value of test no 40                 :  4.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.83
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.29
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.70
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.52
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.79
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.73
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.99
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.80
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.14
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.64
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.22
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.69
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.97
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.04
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908107
   j =  2                              :            45942
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907700
   j =  2                              :            46144
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
 p-value of test no 110                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 111                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 118                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.96
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.50
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.58
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.42
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.29
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.06
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.51
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.78
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.39
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.46
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   69.14
 p-value of test no 146                :  7.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.67
 p-value of test no 147                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.18
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.46
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.28
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.91
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.30
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.93
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.35
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.13
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.20
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.31
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.11
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.91
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.43
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.33
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.14
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.56
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.62
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.27
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.57
 p-value of test no 170                :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.38
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.08
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.43
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.35
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.17
 p-value of test no 175                :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.61
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.30
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.94
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.26
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.00
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.15
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.25
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.32
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.82
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.21
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.78
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.73
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.28
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999999206
 
 Normal statistic for number of bits   : -6.28e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.76
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999931214
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    2.40
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 251                :    0.9917
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:24.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       7.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199032840.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27610
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    3.85
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.17
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.94
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.67
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.86
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.21
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.55
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.51
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.09
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1309.26
 p-value of test no 56                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.33
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.62
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.33
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.19
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.53
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4958.67
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908557
   j =  2                              :            45717
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907929
   j =  2                              :            46031
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.24
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.57
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.83
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.63
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.48
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.88
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.84
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.41
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.70
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.51
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.54
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.81
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.97
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.57
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.91
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.47
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.54
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.14
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.38
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.30
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.00
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.74
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.45
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.78
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.96
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.22
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.93
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.88
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.74
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.45
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.09
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.33
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.71
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.23
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.87
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.23
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.22
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.57
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.25
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 213                :    0.9951
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9632.43
 p-value of test no 215                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.42
 p-value of test no 216                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.66
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.61
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.80
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.23
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.80
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.00
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.90
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999990848
 
 Normal statistic for number of bits   :  -0.072
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.49
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999851102
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    2.15
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:19.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200015880.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27611
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1515
 p-value of test no 12                 :  3.2e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334635
   j =  1                              :        599996970
   j =  2                              :             1515
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9941
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    5.58
 p-value of test no 30                 :  1.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     536
 p-value of test no 31                 :    0.9958
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.17
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.99
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.96
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.53
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.58
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.86
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.46
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.68
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.62
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6878.46
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.36
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.66
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.99
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.40
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907959
   j =  2                              :            46013
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46239
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907527
   j =  2                              :            46229
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.75
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.62
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.37
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.79
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.02
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.67
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.35
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.23
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.48
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.018
 p-value of test no 134                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.12
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.93
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.51
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.30
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.22
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.35
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.09
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.12
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.08
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.44
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.52
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.97
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.61
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.79
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.13
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.23
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.02
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.39
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.57
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.38
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.85
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.34
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.13
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.40
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.30
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.07
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.14
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.59
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.71
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.32
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.59
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.76
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.98
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.91
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.31
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.41
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.12
 p-value of test no 217                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 218                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.83
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.34
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3942.11
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.48
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.47
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.27
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.09
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000023785
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000067684
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:48.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           3.2e-5
  68  MatrixRank, L=1000, r=0         0.9993 
  93  HammingCorr, L = 300            0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200933384.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27612
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.20
 p-value of test no 41                 :  2.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.21
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.49
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.22
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.47
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.43
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6854.30
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.36
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.66
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.20
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.97
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.35
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907952
   j =  2                              :            46024
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907585
   j =  2                              :            46206
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 81                 :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
 p-value of test no 94                 :    0.9941
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.78
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.77
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.60
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.02
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.11
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.70
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.32
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.65
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.36
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.29
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17567.39
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.36
 p-value of test no 146                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.17
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.69
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.79
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.13
 p-value of test no 150                :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.90
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.78
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.73
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.65
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.84
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.10
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.45
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.44
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.88
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.40
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.23
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.94
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.41
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.96
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.35
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.55
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.25
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.19
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.34
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.27
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.31
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.84
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.70
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.16
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.99
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.17
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.11
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.60
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.34
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.50
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.50
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.37
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.81
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.98
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.65
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.83
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.03
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.25
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.85
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999931766
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.01
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999941270
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:46.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201883656.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27613
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7103
 p-value of test no 20                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    4.70
 p-value of test no 24                 :  4.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.39
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.81
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.89
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.13
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.25
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.75
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1562.16
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.59
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.59
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.48
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.84
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5142.33
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908542
   j =  2                              :            45729
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46336
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870336
   j =  1                              :        399907329
   j =  2                              :            46334
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.36
 p-value of test no 118                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.81
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.86
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.16
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.51
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.63
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.03
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.33
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.99
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.58
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.98
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.87
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.81
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.72
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.42
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.25
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.60
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.28
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.91
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.28
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.82
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.28
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.80
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.97
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.21
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.02
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.54
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.42
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.69
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.20
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.09
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.91
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.24
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.20
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.61
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.62
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.88
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.67
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.37
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.68
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.54
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.63
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.22
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11576.01
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.80
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999952484
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.94
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999749156
 
 Normal statistic for number of bits   :   -1.98
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202899464.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27614
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.63
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    3.85
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.01
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.96
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.93
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.54
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.21
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.56
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.95
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.38
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.70
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.76
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.61
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.08
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.78
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.50
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908289
   j =  2                              :            45854
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907814
   j =  2                              :            46090
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.10
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.42
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.74
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.42
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.22
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.05
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.17
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.43
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.43
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.91
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.49
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.35
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.21
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.50
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.32
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.32
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.52
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.10
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.06
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.01
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.99
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.28
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.09
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.33
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.27
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.73
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.95
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.81
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.35
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.23
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.88
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.58
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.02
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.23
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.55
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.65
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.22
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.63
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.85
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.12
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.86
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.31
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.63
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.95
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.67
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.57
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.49
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.55
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11508.24
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.71
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.99
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000040945
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.50
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999938945
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:18.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203882504.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27615
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.66
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.26
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.34
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.43
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.81
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.49
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.31
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.40
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.95
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.91
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.43
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.66
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.99
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.14
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.95
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.70
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908318
   j =  2                              :            45838
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908145
   j =  2                              :            45920
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
 p-value of test no 90                 :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.41
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.32
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.29
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.50
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.10
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.97
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17776.20
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.85
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.06
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.45
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.35
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.94
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.91
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.44
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.21
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.63
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.55
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.82
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.57
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.17
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.45
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.28
 p-value of test no 162                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.37
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.52
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.52
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.36
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.07
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.37
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.84
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  136.52
 p-value of test no 170                :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.12
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.23
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.87
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.80
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.80
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.75
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.30
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 186                :    0.9948
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.53
 p-value of test no 188                :    0.9942
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.36
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.98
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.03
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.82
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.79
 p-value of test no 217                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9923
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.98
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.91
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.62
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.46
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.90
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11514.69
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.87
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999972794
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.52
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000070981
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:57.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 C (L=10000, r=0)    0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204898312.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27616
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.89
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.55
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.22
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.49
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.70
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.31
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.04
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.34
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.49
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.45
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.21
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.49
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908324
   j =  2                              :            45829
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907737
   j =  2                              :            46127
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.32
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.66
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.59
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.55
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.93
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.96
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.78
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.84
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.15
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.71
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17608.43
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.46
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.41
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.19
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.91
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.37
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.57
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.84
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.30
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.82
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.12
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.75
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.19
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.81
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.80
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.35
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.58
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.07
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.62
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.51
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.82
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.54
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.26
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.17
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.85
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.16
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.62
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.58
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    2.55
 p-value of test no 184                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-4
 p-value of test no 190                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.11
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.25
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.56
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.94
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.41
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.80
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.73e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.90
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.01
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.82
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.33
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.98
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.40
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.14
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000026644
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.53
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999955931
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    2.17
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 250                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:49.85
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205914120.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27617
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.78
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9992    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.35
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.44
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.66
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.82
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.06
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.91
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.23
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.24
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.83
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.26
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.97
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.04
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.66
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46070
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870070
   j =  1                              :        399907861
   j =  2                              :            46068
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908747
   j =  2                              :            45622
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9925
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9932
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.15
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.40
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.24
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.11
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.91
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.18
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.56
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.53
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.39
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.04
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.12
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.54
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.86
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.81
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.47
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.00
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.00
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.75
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.08
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.90
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.55
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.83
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.15
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.29
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.39
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.81
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.34
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.36
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.99
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.14
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.31
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.85
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.61
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.96
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.83
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.55
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.33
 p-value of test no 177                :    0.9900
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.58
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.97
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.34
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.39
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.23
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.48
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.76
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.60
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.94
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.37
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.47
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.53
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.97
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.63
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999977387
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.57
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000075307
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:04.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207224840.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27618
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 15                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    4.11
 p-value of test no 38                 :  7.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.42
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.22
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.12
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.61
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.38
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.40
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.06
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.29
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.95
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.03
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.66
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.29
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.08
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908332
   j =  2                              :            45828
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45331
 p-value of test no 71                 :    0.9948
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869331
   j =  1                              :        399909340
   j =  2                              :            45327
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.62
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.23
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.41
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.35
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.79
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.25
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.00
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.64
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.58
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17150.18
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.56
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.48
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.92
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.55
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.85
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.91
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.87
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.46
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.74
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.03
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.01
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.76
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.24
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.43
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.57
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.80
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5142.83
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.18
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.39
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.04
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.52
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4732.49
 p-value of test no 173                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.29
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.85
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.50
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.65
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.58
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.88
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.39
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.08
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.69
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.57
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.45
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.73
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.96
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11571.33
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.34
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.05
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999862364
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.83
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000057130
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:29.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208240648.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27619
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.54
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.05
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.43
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.40
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.19
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.08
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.18
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.45
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.12
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.59
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.38
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.70
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.25
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.77
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907982
   j =  2                              :            46003
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907938
   j =  2                              :            46022
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.81
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.68
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.57
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.11
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.95
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.85
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.36
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.46
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.28
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.94
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.58
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17230.10
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.55
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.63
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.47
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.18
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.87
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.20
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.77
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.78
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.07
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.86
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.67
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.01
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.98
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.05
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.51
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.79
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.77
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.85
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.45
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.30
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.94
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.00
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.09
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.43
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.80
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.34
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.47
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.04
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.79
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.48
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.94
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.44
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.63
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.30
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.93
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.20
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.87
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3891.44
 p-value of test no 228                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.53
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11559.45
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.74
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000002926
 
 Normal statistic for number of bits   :   0.023
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.80
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000059704
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.095
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:05.34
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209289224.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27620
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5528
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    3.82
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.06
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.78
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.58
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.86
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.71
 p-value of test no 52                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.85
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.69
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.25
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.29
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.80
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.57
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.34
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.10
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.25
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907783
   j =  2                              :            46098
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908209
   j =  2                              :            45891
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 94                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.24
 p-value of test no 119                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.37
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.65
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.01
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.35
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.19
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.49
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.33
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.17
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.23
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17420.46
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.68
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.29
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.54
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.65
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.97
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.25
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.13
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.22
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.35
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.28
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.02
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.57
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.06
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.41
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.58
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.58
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.94
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.81
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.60
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.80
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.26
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.03
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.52
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.85
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.84
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.61
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.46
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.36
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.70
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.78
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.50
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.32
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.73
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.76
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.51
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.89
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 224                :    0.9932
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.12
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.76
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.42
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.32
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.65
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.40
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999840140
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.57
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999906629
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:43.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189169673.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27621
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9925
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.18
 p-value of test no 41                 :  7.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.41
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.82
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.73
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.44
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.16
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.43
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.87
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7229.87
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.63
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.35
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.30
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.14
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.36
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908517
   j =  2                              :            45734
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908584
   j =  2                              :            45705
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.08
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.62
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.69
 p-value of test no 121                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.77
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.91
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.81
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.00
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.29
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.54
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.19
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.80
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.90
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.73
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.66
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.57
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.28
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.11
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.62
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.52
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.69
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.41
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.30
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.84
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.57
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.69
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.11
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.35
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.31
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.21
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.68
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.99
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.63
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.32
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.70
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.28
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.95
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.11
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    2.15
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.23
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.23
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.74
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 204                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.74
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.28
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.91
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.53
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.83
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.24
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.25
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.29
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.26
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.94
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999996218
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.69
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999812894
 
 Normal statistic for number of bits   :   -1.48
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:29.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190054409.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27622
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5551
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.60
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.57
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.47
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.56
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.37
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.57
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.36
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6775.15
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.48
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.82
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.72
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.87
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908915
   j =  2                              :            45535
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907954
   j =  2                              :            46020
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.01
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.67
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.06
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.63
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.24
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.09
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.59
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.51
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.23
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.16
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.92
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.48
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.16
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.39
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.76
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.79
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.71
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.08
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.95
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.43
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.61
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.71
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.43
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.89
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.74
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.14
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.82
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.11
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.14
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.18
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.76
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.38
 p-value of test no 171                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.86
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.92
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.78
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.86
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.04
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.74
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.62
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.33
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.85
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.06
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.49
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.25
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.66
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.39
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.73
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.55
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.41
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.91
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999961865
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.67
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999830339
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:43.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191102985.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27623
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7549
 p-value of test no 15                 :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.89
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.86
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.03
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.73
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.66
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.53
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.88
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.51
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.71
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.55
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.38
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.67
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.99
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908030
   j =  2                              :            45982
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908386
   j =  2                              :            45804
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 116                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.48
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.00
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.21
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.83
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.64
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.17
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.69
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17569.09
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.45
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.68
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.78
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.91
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.96
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.17
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.38
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.16
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.28
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.23
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.95
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.25
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.15
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.58
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.74
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.64
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.06
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.35
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.98
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.04
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.23
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.01
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.11
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.65
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.29
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.36
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.05
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.84
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.38
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.21
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.21
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.76
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.75
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.41
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.89
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.25
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.52
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000060883
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.72
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999898007
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:23.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192806921.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27624
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.72
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.92
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.37
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.24
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.51
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.11
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.36
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.47
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.17
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.06
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.97
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.89
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.32
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908124
   j =  2                              :            45932
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46150
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907702
   j =  2                              :            46146
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.59
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.46
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.84
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.30
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.68
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.02
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.02
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.73
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.86
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.88
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.90
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.56
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.93
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.46
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.15
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.77
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.31
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.02
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.31
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.84
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.92
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.31
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.45
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.00
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.28
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.61
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.89
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.27
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.73
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.55
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.31
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.44
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.19
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.79
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.25
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.43
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.62
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.091
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.75
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.66
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.77
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10274.52
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.81
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5042.76
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.92
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.32
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.15
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.23
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.35
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.44
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999973532
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999806315
 
 Normal statistic for number of bits   :   -1.53
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.036
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:06.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193789961.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27625
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 7                  :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.26
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.01
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.92
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.69
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.84
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.88
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.91
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.51
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7376.05
 p-value of test no 57                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.25
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.07
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.82
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5290.78
 p-value of test no 68                 :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908057
   j =  2                              :            45970
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908077
   j =  2                              :            45960
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.21
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.76
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.52
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.30
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.20
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.63
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.98
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.26
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.81
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.49
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.27
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.76
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.99
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.16
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.88
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.33
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.71
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.04
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.77
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.02
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.64
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.45
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.06
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.16
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.86
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.00
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.74
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.39
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.03
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.81
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.61
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.66
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.03
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.46
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.58
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.74
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.41
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.90
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.64
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.13
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.94
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.07
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.71
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.65
 p-value of test no 216                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.45
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.06
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.41
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.31
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.99
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.14
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.04
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999958013
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.53
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999982565
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:50.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194740233.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27626
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.20
 p-value of test no 22                 :  2.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.45
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.97
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.28
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.93
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.55
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.37
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.24
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.84
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.47
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.77
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.14
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.58
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4833.58
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45478
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869478
   j =  1                              :        399909048
   j =  2                              :            45470
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.22
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.24
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.45
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.52
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.11
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.09
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.06
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.90
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.54
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.04
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.66
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.10
 p-value of test no 150                :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.59
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.06
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.26
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.06
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.23
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.97
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.40
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.57
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.89
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.96
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.94
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.87
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.50
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.26
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.18
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.11
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.10
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.39
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.13
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.30
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.61
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.48
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.29
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.01
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.55
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.74
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.84
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.03
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.54
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.66
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.74
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.01
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.63
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.46
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.45
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12091.64
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.54
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000126415
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.91
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999999386
 
 Normal statistic for number of bits   : -4.85e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:11.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195559433.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27627
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.67
 p-value of test no 41                 :  1.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.71
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.09
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.97
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.57
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.09
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.63
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.34
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.79
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.88
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.47
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.16
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.19
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.59
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908701
   j =  2                              :            45639
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908171
   j =  2                              :            45907
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-5
 p-value of test no 112                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.26
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.28
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.15
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.58
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.35
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.46
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.86
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.07
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17466.60
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.02
 p-value of test no 146                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.45
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.25
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.61
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.16
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.06
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.87
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.06
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.55
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.00
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.46
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.46
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.76
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.43
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.09
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.76
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.07
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.67
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.93
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.35
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.68
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.58
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.91
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.79
 p-value of test no 172                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.28
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.86
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.13
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.75
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.48
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.12
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.89
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.05
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.92
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.99
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.45
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5063.77
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.44
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.06
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.55
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.17
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.12
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999893045
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.61
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000194341
 
 Normal statistic for number of bits   :    1.54
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:14.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196706313.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27628
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.74
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.98
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.43
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.72
 p-value of test no 53                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.87
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.94
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.25
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.29
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.27
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.22
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.12
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4924.47
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907934
   j =  2                              :            46027
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907571
   j =  2                              :            46210
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.37
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.93
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.89
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.25
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.80
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.68
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.93
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.86
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.40
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.16
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.96
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.86
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.34
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.34
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.13
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.43
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.11
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.32
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.26
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.85
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.96
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.55
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.67
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.97
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.81
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.46
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.58
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.12
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.49
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.66
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.88
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.59
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.71
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.86
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.87
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.34
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.88
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.33
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.78
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.52
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.92
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.71
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.02
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.68
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.77
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.03
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.40
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999900206
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.15
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000043969
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:16.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197656585.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27629
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 12                 :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7527
 p-value of test no 18                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    4.62
 p-value of test no 32                 :  4.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.16
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.04
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.05
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.60
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.73
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.16
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.09
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.83
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.04
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.67
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.19
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.90
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.75
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.81
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46280
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870280
   j =  1                              :        399907444
   j =  2                              :            46272
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907732
   j =  2                              :            46128
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.01
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.50
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.10
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.99
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.57
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.22
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.53
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.39
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.097
 p-value of test no 134                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.28
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.52
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.83
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.31
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.68
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.79
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.90
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.56
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.46
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.30
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.02
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.58
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  594.98
 p-value of test no 158                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.97
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.06
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.74
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.37
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.15
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.39
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.61
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.09
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.53
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.27
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.59
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.76
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.08
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.01
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.88
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.75
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.25
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.30
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.48
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.23
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.61
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.83
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.64
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.01
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.31
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.03
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.85
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.00
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.94
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.71
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000062026
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.78
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999926528
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:48.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198869001.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27630
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5528
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    3.34
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.20
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.69
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.37
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.50
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.61
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.99
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.19
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1336.18
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.87
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.74
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.77
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.66
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.48
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908257
   j =  2                              :            45867
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908444
   j =  2                              :            45772
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.51
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.18
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.48
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.62
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.54
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.15
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.05
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.48
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.62
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.50
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.80
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.96
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.51
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.66
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.42
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.20
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.08
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.68
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.69
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.97
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.03
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.83
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.93
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.50
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.07
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.63
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.84
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.48
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.76
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.29
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.14
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.55
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.29
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.56
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.34
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.96
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.19
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.71
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.85
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.50
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.28
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.72
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.48
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.87
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.61
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.97
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.07
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.26
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.54
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.21
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999985919
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.28
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999891260
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:40.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199819273.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27631
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    4.78
 p-value of test no 42                 :  3.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.77
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.28
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.50
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.14
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.10
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.79
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.21
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.86
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.16
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.53
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.11
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.75
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.35
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45600
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908802
   j =  2                              :            45596
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907966
   j =  2                              :            46011
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 108                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.51
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.75
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.87
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.13
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.73
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.76
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.12
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.16
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17527.43
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.23
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.59
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.44
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.12
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.86
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.18
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.51
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.65
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.87
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.30
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.73
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.91
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.56
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.23
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.10
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.41
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.45
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.27
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.57
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.61
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.97
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.11
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.18
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.64
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.36
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.75
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.26
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.98
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.16
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.90
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.52
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.81
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 210                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.57
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.52
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.20
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.11
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.82
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.08
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.47
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.52
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.32
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000010792
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.94
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999872534
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    2.52
 p-value of test no 244                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 253                :    0.98
 
 Sample variance                       :    2.33
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:40.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200802313.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27632
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7517
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.91
 p-value of test no 23                 :  9.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.74
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.55
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.28
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.96
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.86
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.65
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.94
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.25
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.22
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.92
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.77
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.89
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.29
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.19
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908307
   j =  2                              :            45845
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907746
   j =  2                              :            46124
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.42
 p-value of test no 119                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.16
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.31
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.83
 p-value of test no 123                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.48
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.54
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.19
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.31
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.088
 p-value of test no 135                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.32
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.66
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.97
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.02
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.15
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.56
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.56
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.99
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.01
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.32
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.86
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.62
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.22
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.33
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.04
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.47
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.67
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.50
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.42
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.71
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.82
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.02
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.62
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.87
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.58
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.32
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.32
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.71
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.26
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.49
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.80
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.96
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.04
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.66
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.07
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
 p-value of test no 220                :    0.9962
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4620.65
 p-value of test no 222                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.34
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.81
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.66
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.96
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.26
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.34
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999945356
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.89
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000173038
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:34.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202113033.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27633
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7109
 p-value of test no 18                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.04
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.14
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.85
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.71
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.84
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.38
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.47
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.05
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.55
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.63
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5160.16
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907875
   j =  2                              :            46052
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908312
   j =  2                              :            45841
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.03
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.93
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.90
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.08
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.42
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.78
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.59
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.21
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.60
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.07
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17261.97
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.15
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.80
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.13
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.35
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.75
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.16
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.82
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.29
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.66
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.96
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.93
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.45
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.22
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.53
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.61
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.01
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.66
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.51
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.43
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.34
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.55
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.44
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.26
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.45
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.45
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.56
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.53
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.57
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.66
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.05
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
 p-value of test no 180                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.53
 p-value of test no 183                :  5.8e-3
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.22
 p-value of test no 196                :  9.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.31
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.11
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.04
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.54
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.28
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.85
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.67
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.99
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.70
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12126.77
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.60
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.60
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999926795
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.73
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000162835
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:02.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203194377.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27634
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.73
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.08
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.54
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.73
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.82
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.39
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.03
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.05
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.73
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.60
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.90
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.19
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.29
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46283
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870283
   j =  1                              :        399907437
   j =  2                              :            46277
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908242
   j =  2                              :            45870
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 85                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.72
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.62
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.77
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.91
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.23
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.13
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.45
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.54
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.76
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.25
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.16
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.97
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.88
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.81
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.68
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.46
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.01
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.23
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.16
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.68
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.56
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.93
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.15
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.33
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.79
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.94
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.63
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.24
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.30
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.01
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.83
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.50
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.12
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.05
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.54
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.10
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.13
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.24
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.13
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10341.37
 p-value of test no 215                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 216                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.95
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5034.74
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.91
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.45
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.96
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11470.00
 p-value of test no 230                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.20
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999974537
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.36
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000063760
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:45.19
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204406793.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27635
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5534
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4186
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.62
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.25
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.42
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.00
 p-value of test no 51                 :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.77
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.45
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.84
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.34
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.34
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.84
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.12
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.62
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.94
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907752
   j =  2                              :            46112
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46295
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870295
   j =  1                              :        399907414
   j =  2                              :            46287
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.77
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.88
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.95
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.79
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.13
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.55
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.61
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.40
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.60
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.37
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.12
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.25
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.16
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.02
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.96
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.71
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.24
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.67
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.27
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.68
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.29
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.95
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.87
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.91
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.96
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.37
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.64
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.52
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.16
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.73
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.26
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4759.85
 p-value of test no 168                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.42
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.41
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.14
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.51
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.67
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.10
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.56
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.22
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.96
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.54
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.96
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.89
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.16
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.41
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.47
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.043
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.87
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.00
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.50
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.34
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.80
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.95
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.78
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000063289
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.37
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000081241
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:19.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205422601.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27636
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5251
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 26                 :    0.9991    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.68
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.40
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.88
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.71
 p-value of test no 51                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.25
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.34
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.07
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.54
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.66
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.83
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.46
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.93
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.14
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908090
   j =  2                              :            45952
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45480
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909041
   j =  2                              :            45478
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.95
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.89
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.13
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.97
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.69
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.68
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.00
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.55
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17522.08
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.43
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.35
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.78
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.37
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.02
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.54
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.27
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.49
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.62
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.00
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.27
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.72
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.42
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.34
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.23
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.96
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.66
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.75
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.05
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.32
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.65
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.62
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.82
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.24
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.17
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.74
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.57
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.44
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.24
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.46
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.73
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.62
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.65
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.29
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.91
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.17
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.37
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.61
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.38
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.36
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000031252
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.47
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000207466
 
 Normal statistic for number of bits   :    1.64
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.069
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.030
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:23.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206569481.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27637
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997303
   j =  2                              :             1347
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 12                 :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7117
 p-value of test no 20                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.22
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.59
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.68
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.41
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.22
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.85
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.43
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.79
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6867.76
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.94
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 63                 :  6.0e-4    *****
 
 Anderson-Darling statistic = A2       :    7.82
 p-value of test no 64                 :  1.5e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  104.53
 p-value of test no 65                 :  3.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.79
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.57
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908187
   j =  2                              :            45899
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908028
   j =  2                              :            45980
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.40
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.36
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.14
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.29
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.60
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.56
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.49
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.35
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.93
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.70
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.55
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.21
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.85
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.19
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.36
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.70
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.75
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.44
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.21
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.58
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.28
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.72
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.37
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.82
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.79
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.02
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.41
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.43
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.00
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.27
 p-value of test no 170                :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.72
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.26
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.56
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.45
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.68
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.44
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.48
 p-value of test no 196                :    0.9931
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.39
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.21
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.16
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.16
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.48
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.84
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.90
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.61
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12126.37
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.64
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.94
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000044746
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.16
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999943073
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:14.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           9.4e-4
  39  Run, r = 15                     3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207618057.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27638
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9931
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.51
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.55
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.70
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.24
 p-value of test no 51                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.87
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.39
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.61
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.66
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.05
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.69
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.10
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.99
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.53
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.39
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908433
   j =  2                              :            45779
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908233
   j =  2                              :            45876
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.34
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.59
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.58
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.24
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.29
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.56
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.73
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.46
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.24
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.07
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.41
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.47
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.11
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.73
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.88
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.19
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.87
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.48
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.93
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.23
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.99
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.12
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.74
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.52
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.36
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.29
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.41
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.42
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.19
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.15
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.61
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.31
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.87
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.94
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.97
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.39
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.40
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.31
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.87
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.73
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.42
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.68
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.38
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.93
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.27
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.43
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.26
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11551.22
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.96
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000043771
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.46
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999912854
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:40.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208568329.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27639
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 9                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    3.64
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.40
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.95
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.53
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.74
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.18
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.66
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.09
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.73
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.93
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 58                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.17
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.07
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.45
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.95
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908088
   j =  2                              :            45953
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907700
   j =  2                              :            46144
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 116                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.84
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.42
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.54
 p-value of test no 121                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.80
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.07
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.26
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.38
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.89
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.45
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.75
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.055
 p-value of test no 135                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.67
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.60
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.38
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.90
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.28
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.78
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.12
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.94
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.44
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.40
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.46
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.17
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.36
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.97
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.15
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.15
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.01
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.72
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.26
 p-value of test no 165                :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.74
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.68
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.28
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.65
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.27
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.87
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.81
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.92
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.37
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.44
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.95
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.90
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.42
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.67
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.78
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.43
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.48
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.18
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.40
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.69
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.32
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.51
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.98
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000071353
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.92
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000001456
 
 Normal statistic for number of bits   :   0.012
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:58:03.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209616905.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27640
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 7                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 10                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 11                 :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7107
 p-value of test no 15                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.35
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.14
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.87
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.66
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.50
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.10
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.08
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.84
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.94
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.35
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.45
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.80
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908570
   j =  2                              :            45712
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45499
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869499
   j =  1                              :        399909003
   j =  2                              :            45497
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.36
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.58
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.72
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.93
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.02
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.91
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.26
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.30
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17092.28
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.99
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.82
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.41
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.48
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.09
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.13
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.29
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.84
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.85
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.19
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.44
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.73
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.79
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.45
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.56
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.08
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.76
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.50
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.20
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.32
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.64
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.37
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.85
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.05
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4760.89
 p-value of test no 173                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.75
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.88
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.15
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.07
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.98
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.02
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.76
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.32
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.34
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.23
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.99
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.81
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.14
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.87
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000008341
 
 Normal statistic for number of bits   :   0.066
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.06
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000068836
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:45.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189202442.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27641
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5261
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.39
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.05
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.57
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.13
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.12
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.16
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.30
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.12
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6805.19
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.17
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.90
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.09
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.49
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5192.78
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908351
   j =  2                              :            45817
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908460
   j =  2                              :            45764
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.06
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.38
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.40
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.88
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.78
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.51
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.32
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.28
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.17
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.46
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.29
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17744.40
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.47
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.07
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.57
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.35
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.96
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.09
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.16
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.16
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.40
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.68
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.40
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.00
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.64
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.87
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.15
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.47
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.51
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.93
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.48
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.55
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.69
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  306.53
 p-value of test no 169                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.83
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.79
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.42
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.12
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.05
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.98
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.73
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.21
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.43
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.67
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
 p-value of test no 209                :    0.9964
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9648.34
 p-value of test no 211                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.30
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.46
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.43
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.11
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.62
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.24
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.41
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.54
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999918329
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.23
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000143548
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.077
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:18.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190480394.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27642
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5282
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7088
 p-value of test no 15                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9932
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.77
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.37
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.32
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.24
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.59
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.04
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.68
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.98
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.47
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.00
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.07
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.65
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.07
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.04
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908426
   j =  2                              :            45784
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908777
   j =  2                              :            45607
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.67
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.75
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.00
 p-value of test no 122                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.06
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.01
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.38
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.28
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 132                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.92
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.33
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17118.74
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.01
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.94
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.21
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.21
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.49
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.76
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.54
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.58
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.45
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.30
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.29
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.62
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.72
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.96
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.97
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.97
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.22
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.70
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.13
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.07
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.55
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.38
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.15
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.07
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.74
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.63
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.79
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.72
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.81
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.62
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.56
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.95
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.04
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 214                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9604.81
 p-value of test no 215                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.02
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.35
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.98
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.26
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.47
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12038.01
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.90
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999899096
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   96.37
 p-value of test no 233                :  3.5e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000015742
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:18.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191791114.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27643
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.79
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.37
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.45
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.86
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.60
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.36
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.04
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.96
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.34
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.92
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.76
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.78
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908635
   j =  2                              :            45678
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908296
   j =  2                              :            45846
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-4
 p-value of test no 110                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.72
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.76
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.50
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.77
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.02
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.13
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.04
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.55
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.99
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.06
 p-value of test no 146                :  9.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.56
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.27
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.32
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.05
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.37
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.62
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.36
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.19
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.44
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.85
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.31
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.76
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.02
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.32
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.11
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.13
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.12
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  485.43
 p-value of test no 167                :  3.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.66
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.43
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.67
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.89
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.80
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.48
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.73
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.31
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.55
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.39
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.48
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.27
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.26
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.93
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.77
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.41
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.57
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12088.85
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.04
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.83
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999985454
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.00
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999974315
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:47.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 M (L=10000, r=0)    3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192905226.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27644
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7491
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.16
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.10
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.77
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.57
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.67
 p-value of test no 53                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.13
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.64
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.88
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.19
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.80
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.28
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.80
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.76
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.28
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45563
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869563
   j =  1                              :        399908876
   j =  2                              :            45559
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908469
   j =  2                              :            45761
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.50
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.69
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.87
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.98
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.13
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.32
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.22
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.90
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.45
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.71
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.42
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.23
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.94
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.89
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.51
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.32
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.38
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.94
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.19
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.94
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.86
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.76
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.99
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.71
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.12
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.52
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.59
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.51
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.42
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.18
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.47
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.94
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.80
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.17
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.81
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.49
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.02
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.99
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.22
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.07
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.52
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.97
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.82
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.61
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.72
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.28
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.44
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.85
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.53
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.81
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.44
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.10
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000067108
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.51
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000109519
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:42.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193855498.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27645
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 9                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7553
 p-value of test no 19                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.45
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.81
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.89
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.60
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.16
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.93
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.14
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.38
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.71
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.16
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.47
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.49
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45622
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869622
   j =  1                              :        399908760
   j =  2                              :            45614
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907880
   j =  2                              :            46051
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.24
 p-value of test no 119                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.62
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.65
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.92
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.87
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.90
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.09
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.68
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.11
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.31
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.01
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.66
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.03
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.03
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.83
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.17
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.35
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.43
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.02
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.77
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.03
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.29
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.90
 p-value of test no 161                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.66
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.14
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.02
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.26
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.43
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.84
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.23
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.26
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.68
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.33
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.32
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.97
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.12
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.68
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.07
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.51
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.88
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.10
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.53
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.23
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.98
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.14
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.70
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.06
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.22
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.18
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.14
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999911117
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.95
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999954185
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:04.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194707466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27646
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1248
 p-value of test no 5                  :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334368
   j =  1                              :        599997504
   j =  2                              :             1248
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 32                 :    0.9943
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.65
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.84
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.31
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.14
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.82
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.38
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.58
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.49
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.72
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.19
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.67
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.73
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.99
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5197.49
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908752
   j =  2                              :            45621
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.71
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.02
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.23
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.91
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.26
 p-value of test no 123                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.39
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.95
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.45
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.91
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.40
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.08
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17665.63
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.27
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.36
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.41
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.85
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.19
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.27
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.94
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.95
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.01
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.30
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.16
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.89
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.63
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.77
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.71
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.25
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.93
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.77
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.54
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.66
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.01
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.56
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.82
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.95
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.13
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.60
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.61
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.85
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.57
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.08
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.68
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.91
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.12
 p-value of test no 189                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.42
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.53
 p-value of test no 207                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.35
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.93
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.10
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.99
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.78
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.31
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.91
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.27
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.37
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999926420
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.00
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999913391
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
 p-value of test no 246                :    0.9952
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:53.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195493898.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27647
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.33
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.42
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.82
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.18
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.76
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.04
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.44
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  486.43
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.38
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.60
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.87
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-4
 p-value of test no 62                 :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.73
 p-value of test no 65                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.19
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4915.74
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907978
   j =  2                              :            46008
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908676
   j =  2                              :            45650
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.04
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.85
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.93
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.66
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.04
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.29
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.14
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.91
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.12
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17538.15
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.68
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.83
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.60
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.82
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.69
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.14
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.51
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.25
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.86
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.05
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.53
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.62
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.55
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.30
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.61
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.27
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.25
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.83
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.52
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.86
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.27
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.03
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.00
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.30
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.54
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.74
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.68
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.69
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.47
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-4
 p-value of test no 194                :    0.9950
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.28
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.41
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.42
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.54
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.84
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.04
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.42
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.43
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.37
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12296.65
 p-value of test no 229                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.17
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.50
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999839600
 
 Normal statistic for number of bits   :   -1.27
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.58
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999982046
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:30.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196476938.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27648
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9925
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    3.89
 p-value of test no 38                 :  9.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.66
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.18
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.14
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.29
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.40
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.41
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.24
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.50
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.22
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.71
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.21
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.52
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.14
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.32
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.65
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46649
 p-value of test no 70                 :  1.7e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870649
   j =  1                              :        399906704
   j =  2                              :            46645
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907688
   j =  2                              :            46150
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 117                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.17
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.94
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.57
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.44
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.79
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.46
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.20
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.09
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.47
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.44
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.03
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.77
 p-value of test no 148                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.71
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.81
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.62
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.86
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.00
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.16
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.40
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.51
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.54
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.98
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.94
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.87
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.68
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.97
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.24
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.45
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.96
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.18
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.80
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.49
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.51
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.13
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.99
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.99
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.91
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.35
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.16
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.37
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.06
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.17
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4306.03
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.06
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.21
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.75
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.08
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000011383
 
 Normal statistic for number of bits   :   0.090
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000157342
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.058
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:05.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  44  CollisionPermut, r = 0          1.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197427210.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27649
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9946
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.95
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.77
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.85
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.04
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.57
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.12
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.31
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.85
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.26
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.69
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.11
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.24
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.61
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907918
   j =  2                              :            46038
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908221
   j =  2                              :            45888
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 90                 :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    5.92
 p-value of test no 92                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.59
 p-value of test no 122                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.64
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.18
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.85
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.99
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.02
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17628.99
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.99
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.96
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.55
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    5.96
 p-value of test no 149                : 1 -  6.7e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.23
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.26
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.19
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.20
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.33
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.31
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.89
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.87
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.57
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.99
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.76
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.34
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.92
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  581.70
 p-value of test no 163                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.14
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.80
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.86
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.62
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.00
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.76
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.77
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.42
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.67
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.84
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.48
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.67
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.38
 p-value of test no 178                :  9.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.23
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.89
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.68
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.11
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.81
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.12
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.39
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.54
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.03
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.46
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.27
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.52
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.82
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000084490
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.29
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000046012
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:55.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 R (L=50, r=0)      1 -  6.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198443018.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27650
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1497
 p-value of test no 12                 :  2.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334617
   j =  1                              :        599997006
   j =  2                              :             1497
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 45                 :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.60
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.49
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.32
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.12
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.44
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.14
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.26
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.86
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.42
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.94
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.18
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.98
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.89
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46065
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907874
   j =  2                              :            46057
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908468
   j =  2                              :            45763
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.22
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.91
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.57
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.31
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.86
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.59
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.27
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.74
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.11
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.20
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17538.44
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.19
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.35
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.05
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.09
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.75
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.56
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.44
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.24
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.42
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.78
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.49
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.56
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.59
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.19
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.48
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.93
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.63
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.79
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.98
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.49
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.66
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.45
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.66
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.62
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.19
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.98
 p-value of test no 175                :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.03
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.92
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.86
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.84
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.85
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.58
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.82
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.89
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.99
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.26
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.83
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.61
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.77
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.03
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000110320
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.22
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000018364
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    2.32
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:23.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199426058.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27651
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9916
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.98
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.70
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.79
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.19
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.45
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.75
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.78
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.18
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.13
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.43
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.20
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.81
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.32
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.05
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908246
   j =  2                              :            45871
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908171
   j =  2                              :            45910
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.62e-3
 p-value of test no 107                :    0.9961
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.32
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.34
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.19
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.96
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.49
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.82
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.04
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.78
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.24
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.20
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.54
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17277.10
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.96
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.19
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.63
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.66
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.26
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.49
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.82
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.42
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.89
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.97
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.98
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.81
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.87
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.67
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.31
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.91
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.07
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.23
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.92
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.38
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.01
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.61
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.98
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.23
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.85
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.81
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.71
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.74
 p-value of test no 176                :  1.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 186                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.39
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.81
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.76
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.07
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.22
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.01
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.86
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3957.97
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.50
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12116.92
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.03
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000108121
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.57
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000077212
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 250                :  9.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    4.71
 p-value of test no 252                :  4.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.44
 p-value of test no 253                :    0.9927
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:41.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200441866.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27652
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5271
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9977
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.02
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.06
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.26
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.00
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.10
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.93
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.18
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.07
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.54
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.21
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.73
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.50
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908384
   j =  2                              :            45802
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908593
   j =  2                              :            45699
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 93                 :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.58
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.23
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.00
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.50
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.86
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.69
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.76
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.43
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.13
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17474.79
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.43
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.69
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.36
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.90
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.09
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.51
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.26
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.89
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.57
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.89
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.46
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.43
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.66
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.68
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.74
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.98
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.36
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.75
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.43
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.33
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.56
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4786.92
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.23
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.38
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.88
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.54
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.91
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.42
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.16
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.99
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.97
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.01
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10205.79
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.56
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 218                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.96
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.53
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.74
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.59
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12029.94
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.35
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.87
 p-value of test no 231                :  4.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000144589
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.31
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000068725
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:19.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201523210.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27653
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5266
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     342
 p-value of test no 37                 :  9.3e-3
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.77
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.88
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.24
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.69
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.61
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.97
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.88
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.17
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.33
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.25
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.56
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.38
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.67
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.89
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46353
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870353
   j =  1                              :        399907298
   j =  2                              :            46345
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45491
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869491
   j =  1                              :        399909021
   j =  2                              :            45485
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.68
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.10
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.98
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.77
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.16
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.68
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.02
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.43
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.53
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.95
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17564.73
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.61
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.83
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.47
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.07
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.71
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.69
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.17
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.53
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.97
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.19
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.98
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.43
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.70
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.03
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.95
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.11
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.95
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.48
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.78
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.42
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.94
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.65
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.28
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.89
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.78
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.77
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.01
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.43
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.46
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.69
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 187                :  8.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 188                :    0.9946
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 202                :    0.9995    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.59
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.93
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.43
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.13
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.90
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.81
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.80
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.30
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.55
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.54
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.77
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000035476
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.01
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999962231
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.091
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:25.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202571786.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27654
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 5                  :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4495
 p-value of test no 14                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.35
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.58
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.86
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.21
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.74
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.66
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.46
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.46
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.23
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.01
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.46
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.59
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.45
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908309
   j =  2                              :            45844
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908166
   j =  2                              :            45908
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.16
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.55
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.27
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.04
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.94
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.99
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.63
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.90
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.71
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.65
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.71
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.38
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.79
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.29
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.18
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.81
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.91
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.03
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.28
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.80
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.61
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.50
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.56
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.64
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.82
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.99
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.23
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.37
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.94
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.83
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.16
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.66
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.24
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.98
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4749.29
 p-value of test no 173                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.94
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.85
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.99
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.61
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.79
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 210                :  9.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9638.81
 p-value of test no 211                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.75
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.60
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.65
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.66
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3950.72
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.72
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.55
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.49
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999917744
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.77
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000020278
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:31.51
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203587594.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27655
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 23                 :    0.9978
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.29
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.33
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.14
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.28
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.58
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.10
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  499.88
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.39
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.68
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.16
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.42
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.37
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.94
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.38
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46276
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870276
   j =  1                              :        399907454
   j =  2                              :            46264
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908512
   j =  2                              :            45741
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.41
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.94
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.62
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.35
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.91
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.32
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.85
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.01
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.36
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.98
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.20
 p-value of test no 151                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.81
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.49
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.91
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.04
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.21
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.91
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.55
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.35
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.39
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.85
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.76
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.59
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.88
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.25
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.13
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.98
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.33
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.61
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.14
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.94
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  472.87
 p-value of test no 174                :  6.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.66
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.18
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.62
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.44
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 202                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.75
 p-value of test no 203                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.44
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.64
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.65
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.77
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4706.91
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.98
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.56
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.12
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.68
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.94
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000013603
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.23
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000057472
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:05.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204636170.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27656
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 26                 :    0.9989
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.04
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.61
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.70
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.56
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.39
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.59
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.94
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.35
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.58
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.95
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.97
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.68
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907604
   j =  2                              :            46195
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908583
   j =  2                              :            45704
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.92e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.69
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.05
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.13
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.90
 p-value of test no 122                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.02
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.12
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.04
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.75
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.10
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.97
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.17
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.79
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.20
 p-value of test no 147                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.94
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.10
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.42
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.27
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.36
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.99
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.45
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.10
 p-value of test no 158                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.60
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.79
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.96
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.74
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.53
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.55
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.83
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.65
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.05
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.38
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.64
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.53
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.27
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.04
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4812.92
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.38
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.14
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.63
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.18
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.15
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.73
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.57
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.39
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.55
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.18
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.37
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.65
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000012634
 
 Normal statistic for number of bits   :   0.100
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.35
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999971393
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.055
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:55.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205684746.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27657
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    6.48
 p-value of test no 33                 :  6.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    3.78
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.34
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.46
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.28
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.22
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.80
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.78
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.08
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.80
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.66
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7182.19
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
 p-value of test no 58                 :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.82
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.54
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.57
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.55
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.71
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46274
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870274
   j =  1                              :        399907455
   j =  2                              :            46268
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908068
   j =  2                              :            45960
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 79                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 81                 :  5.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9933
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.29
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.07
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.65
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.49
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.16
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.35
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.14
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.75
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.08
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.35
 p-value of test no 146                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.55
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.95
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.65
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.22
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.64
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.81
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.70
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.59
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.08
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.41
 p-value of test no 156                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.67
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.37
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.79
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.90
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.20
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.32
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.44
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.14
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.93
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.49
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.58
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.18
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.91
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.05
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.75
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.45
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5199.03
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.44
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.49
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.10
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.60
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.99
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.81
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.46
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.65
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.41
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.67
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 225                :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.44
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.62
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.06
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.73
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.59
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.88
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000011059
 
 Normal statistic for number of bits   :   0.087
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.41
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000028594
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:27.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         6.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206733322.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27658
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1524
 p-value of test no 12                 :  1.1e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334644
   j =  1                              :        599996952
   j =  2                              :             1524
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.03
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.75
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.72
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.70
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.76
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.66
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.01
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.14
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.70
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.45
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908426
   j =  2                              :            45781
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907699
   j =  2                              :            46143
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.45
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.12
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.09
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.95
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.65
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.81
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.65
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.32
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.27
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.80
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.70
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.06
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.00
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.54
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.63
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.11
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.72
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.33
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.90
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.42
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.60
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.07
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.93
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.29
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.05
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.96
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.16
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.03
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.67
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.91
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.40
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.97
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.30
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.76
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5183.72
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.32
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.02
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.62
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.29
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.28
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.52
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.93
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.68
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.97
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.07
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.12
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.61
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.38
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999956852
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.20
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999957062
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.97
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:28.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207781898.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27659
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 29                 :    0.9952
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.09
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.61
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.31
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.66
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.49
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.21
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.83
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.28
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.66
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.19
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.14
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.34
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.76
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.55
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.76
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5274.57
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908402
   j =  2                              :            45790
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908847
   j =  2                              :            45575
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.96
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.82
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.74
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.53
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.65
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.17
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.76
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.22
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.11
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.87
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.84
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.84
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.83
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.63
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.11
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.97
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.85
 p-value of test no 154                :    0.9900
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.45
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.83
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.39
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.54
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.44
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.91
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.61
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.84
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.48
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.24
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.73
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.68
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.13
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.44
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.28
 p-value of test no 171                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.69
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5254.61
 p-value of test no 173                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.52
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.81
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.32
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.80
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 195                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.59
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.48
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.02
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.22
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.43
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5126.47
 p-value of test no 226                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.74
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.17
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.83
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12124.33
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.38
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000022588
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.61
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000013198
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 251                :  8.8e-3
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:44.76
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208797706.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27660
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.95
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.49
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.41
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.95
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.01
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.47
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.09
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7196.08
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.78
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.30
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.41
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.14
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.90
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908734
   j =  2                              :            45630
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908023
   j =  2                              :            45984
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.06
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.92
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.67
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.79
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.57
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.96
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.63
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.68
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.04
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17285.74
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.39
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.51
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.96
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.89
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.51
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.39
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.66
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.95
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.41
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.90
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.96
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.51
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.78
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.31
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.97
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.46
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.00
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.68
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.34
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.00
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.94
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.45
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.92
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.91
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.43
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.40
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.21
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.64
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.84
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    2.37
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.82
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.33
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.02
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.08
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10249.09
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.60
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.26
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.34
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.44
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.26
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12192.66
 p-value of test no 230                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.82
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999901139
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.90
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000087475
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 235                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    5.95
 p-value of test no 237                :  1.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.30
 p-value of test no 238                :    0.9995    *****
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 242                :    0.9986
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:58.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189235211.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27661
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 9                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.99
 p-value of test no 44                 :  8.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.82
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.78
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.08
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.85
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.97
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.09
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.38
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.07
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.14
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.67
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.17
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.06
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.74
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908314
   j =  2                              :            45837
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46179
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870179
   j =  1                              :        399907646
   j =  2                              :            46171
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-6
 p-value of test no 109                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.03
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.11
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.94
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.14
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.17
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.85
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.59
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.16
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.085
 p-value of test no 135                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.99
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17688.56
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.56
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.26
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.18
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.48
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.43
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.89
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.69
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.63
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.39
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.81
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.43
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.87
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.14
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.67
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.16
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.17
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.65
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.56
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.34
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.96
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.29
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.90
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.40
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.70
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.85
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.69
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.21
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.78
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.40
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.72
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.81
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.84
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.90
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.33
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.98
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.49
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.87
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.00
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000104509
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.07
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999910049
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 235                :  6.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 237                :  8.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.44
 p-value of test no 238                :    0.9927
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    2.13
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:44.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189988875.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27662
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5540
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.12
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9931
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.32
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.93
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.88
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.44
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.93
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.94
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1544.94
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.14
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.53
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.23
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.18
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.16
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.96
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908408
   j =  2                              :            45790
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908744
   j =  2                              :            45622
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 97                 :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.64
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.09
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.69
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.82
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.53
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.89
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.24
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.21
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.09
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17578.18
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.90
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.10
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.52
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.54
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.16
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.66
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.53
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.21
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.70
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.96
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.68
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.28
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.08
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.22
 p-value of test no 161                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.04
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.91
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.17
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.71
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.58
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.79
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.69
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.63
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.07
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.55
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.07
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.05
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.55
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.51
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.78
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 181                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.58
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.02
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.31
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.26
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.88
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.81
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.26
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.20
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.78
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.77
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.95
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999957020
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.37
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000213286
 
 Normal statistic for number of bits   :    1.69
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
 p-value of test no 235                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 237                :  8.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.79
 p-value of test no 238                :  2.7e-3
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.029
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:01.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191070219.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27663
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.92
 p-value of test no 35                 :  9.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.48
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.06
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.82
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.83
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.35
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.24
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.97
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.95
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.85
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.73
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.87
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.56
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4852.86
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46273
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870273
   j =  1                              :        399907460
   j =  2                              :            46261
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908135
   j =  2                              :            45925
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
 p-value of test no 100                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.01
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.39
 p-value of test no 120                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.43
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.46
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.69
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.84
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.63
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.96
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.22
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.19
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.55
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.24
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.90
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.01
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.67
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.58
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.32
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.20
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.17
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.55
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.83
 p-value of test no 159                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.13
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.83
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.59
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.07
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.08
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.86
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.39
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.31
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.49
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.70
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.48
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.81
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.32
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.40
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.29
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.48
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.96
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.43
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.38
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.57
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.80
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.22
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.13
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.41
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.66
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.64
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.55
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999845927
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.03
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999962903
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:59.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192020491.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27664
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 4                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.32
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.00
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.61
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.38
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.44
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.77
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.81
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.94
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.70
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.02
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.38
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.77
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.90
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.32
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.97
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908630
   j =  2                              :            45679
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908321
   j =  2                              :            45835
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 90                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 104                :    0.9939
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.46
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.94
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.45
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.63
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.03
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.49
 p-value of test no 124                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.20
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.40
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.60
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.00
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.76
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.85
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.21
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.72
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.51
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.21
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.50
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.43
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.75
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.13
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.74
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.51
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.98
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.34
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.15
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.24
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.46
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.15
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.94
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.24
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.57
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.61
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.91
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.55
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.21
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.35
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.05
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.40
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.26
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.88
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 185                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    5.56
 p-value of test no 187                :  1.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 188                :    0.98
 
 Sample variance                       :    2.85
 p-value of test no 189                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.03
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.83
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.36
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.10
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.16
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.67
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 223                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 224                :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4642.69
 p-value of test no 226                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.28
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.35
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.14
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.29
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000004588
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.95
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000018799
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-3
 p-value of test no 251                :    0.9988
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.41
 p-value of test no 253                :    0.9921
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:39.42
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193069067.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27665
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.60
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.02
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.55
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.29
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.83
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.56
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.10
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.59
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.68
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6935.83
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.89
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.11
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.23
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.28
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5223.83
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908216
   j =  2                              :            45889
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907774
   j =  2                              :            46104
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.53
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.87
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.73
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.09
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.80
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.24
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.23
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.70
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.21
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.47
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.33
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.97
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.16
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.75
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.25
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.13
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.28
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.35
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.86
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.53
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.44
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.24
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.42
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.63
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.72
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.39
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.43
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.91
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.01
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.99
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.61
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.60
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.20
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.10
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  261.08
 p-value of test no 175                :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.25
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.41
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 210                :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.75
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.53
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5090.49
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.57
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.77
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.98
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.42
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11630.26
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.37
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999884939
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.06
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000114583
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    2.45
 p-value of test no 239                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:32.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194117643.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27666
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9956
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.45
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.85
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.25
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.40
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.91
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.80
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.93
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.50
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.67
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.20
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.76
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.29
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908120
   j =  2                              :            45937
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907599
   j =  2                              :            46199
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 86                 :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 104                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.48
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.24
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.85
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.22
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.40
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.64
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.03
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.92
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17270.41
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.83
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.78
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.39
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.68
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.48
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.78
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.21
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.49
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.21
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.96
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.00
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.88
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.61
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.85
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.49
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.59
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.84
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.82
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.43
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.33
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.58
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.22
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.79
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.58
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.83
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.36
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.59
 p-value of test no 175                :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.54
 p-value of test no 196                :  2.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 202                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  145.59
 p-value of test no 203                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.15
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.02
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.47
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.07
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.71
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.86
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.88
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.39
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12229.94
 p-value of test no 230                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.82
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000093049
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.37
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999962618
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:07.17
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195264523.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27667
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1248
 p-value of test no 9                  :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334368
   j =  1                              :        599997504
   j =  2                              :             1248
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5150
 p-value of test no 13                 :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.49
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.60
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.71
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.94
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.24
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.87
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.41
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.45
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.95
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.53
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.04
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.67
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.95
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.45
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.64
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.39
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46355
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870355
   j =  1                              :        399907292
   j =  2                              :            46351
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907928
   j =  2                              :            46030
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.51
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.04
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.61
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.85
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.92
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.94
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.12
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.47
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.75
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.60
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 143                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17780.42
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.89
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.40
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.50
 p-value of test no 149                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.29
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.96
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.11
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.58
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.41
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.20
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.78
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.50
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.90
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.29
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.53
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.63
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.14
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.97
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.48
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.87
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.11
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.42
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.08
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.99
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.28
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.00
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.46
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    2.42
 p-value of test no 184                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.01
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.38
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.32
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.35
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.21
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.76
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.00
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.14
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.62
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.43
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.01
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999962030
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.60
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000038050
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:26.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9993 
  13  BirthdaySpacings, t = 2         0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196280331.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27668
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 11                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.08
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.19
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.23
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.82
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.61
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.56
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.06
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.21
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.71
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.78
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.91
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.47
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908149
   j =  2                              :            45921
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908548
   j =  2                              :            45717
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.06
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.27
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.66
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.50
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.08
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.32
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.99
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.01
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.15
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.85
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.82
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.39
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.53
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.35
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.16
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.44
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.20
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.28
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.37
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.50
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.12
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.20
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.26
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.14
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.22
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.09
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.02
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.30
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.24
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.95
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.97
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.51
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.23
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.47
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.93
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.86
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.58
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.52
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.03
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.74
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.95
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.81
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.96
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.27
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.83
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.27
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.96
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11519.03
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.60
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.54
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000047362
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.25
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999918713
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:06.97
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197394443.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27669
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.71
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.19
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.20
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.00
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.18
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.47
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.15
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.36
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.08
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.92
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7170.76
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   51.75
 p-value of test no 61                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.24
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.35
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.93
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.28
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46273
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870273
   j =  1                              :        399907457
   j =  2                              :            46267
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908149
   j =  2                              :            45918
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.10
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.71
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.77
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.32
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.17
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.51
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.64
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.36
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17171.05
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.20
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.08
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.07
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.77
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.22
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.87
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.70
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.69
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.81
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.61
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.39
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.47
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.76
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.28
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.91
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.48
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.16
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.29
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.34
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.76
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.98
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.90
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.47
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.35
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.98
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.86
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.34
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  304.07
 p-value of test no 174                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.11
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.70
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.91
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 185                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.66
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.94
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.23
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.86
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.25
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.94
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.56
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.23
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.72
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.88
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.73
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.01
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000121300
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.90
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000069418
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.015
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:34.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198508555.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27670
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    3.83
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.49
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.46
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.92
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.91
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.16
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.27
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.15
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.02
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.73
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.26
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.40
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.41
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907665
   j =  2                              :            46160
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46214
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870214
   j =  1                              :        399907574
   j =  2                              :            46210
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.90
 p-value of test no 119                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.04
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.10
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.06
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.24
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.52
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.72
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.03
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.70
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.83
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.39
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.10
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.28
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.22
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.27
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.80
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.77
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.49
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.71
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.31
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.16
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.50
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.80
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.29
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.87
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.65
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.90
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.09
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.99
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.26
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.82
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.05
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.10
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.36
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.18
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.58
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.60
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.74
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 201                :    0.9920
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.06
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-3
 p-value of test no 204                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.91
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.10
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.52
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.82
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.24
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.68
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.99
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.62
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.96
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.69
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000183805
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   97.04
 p-value of test no 233                :  3.0e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999842825
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    2.88
 p-value of test no 239                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:14.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199557131.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27671
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 10                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    3.24
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.65
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.35
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.18
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.20
 p-value of test no 53                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.60
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.58
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.13
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7209.04
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.30
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.79
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.09
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4814.39
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908133
   j =  2                              :            45926
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908393
   j =  2                              :            45793
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.56
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.29
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.78
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.18
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.18
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.64
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.04
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.03
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.40
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.84
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.28
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.55
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.95
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.46
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.95
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.89
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.55
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.14
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.36
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.00
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.95
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.61
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.54
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.96
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.36
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.95
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.09
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.55
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.44
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.42
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.09
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.79
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.60
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.92
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.70
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.66
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.70
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.94
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.35
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.94
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.71
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.38
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.96
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.59
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.95
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11632.92
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.27
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000032419
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.59
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999952754
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:24.65
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200540171.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27672
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 9                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4528
 p-value of test no 16                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    3.09
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.48
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.54
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.00
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.29
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.42
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.88
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.18
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.40
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.35
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.89
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.44
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.84
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.37
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.46
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908452
   j =  2                              :            45768
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45598
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869598
   j =  1                              :        399908807
   j =  2                              :            45592
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.32
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.07
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.86
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.01
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 128                :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.53
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.61
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.54
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.26
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.60
 p-value of test no 146                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.30
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.62
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.85
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.74
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.17
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.89
 p-value of test no 153                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.21
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.90
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.05
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.36
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.62
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.59
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.10
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.67
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.27
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.81
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.17
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.92
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.76
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.03
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.68
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.56
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.56
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.97
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.02
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.09
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.70
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.87
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.81
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.38
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.54
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 205                :    0.9954
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.72
 p-value of test no 207                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 209                :    0.9925
 
 Anderson-Darling statistic = A2       :    6.43
 p-value of test no 210                :  6.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9501.47
 p-value of test no 211                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.45
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.81
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.80
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.54
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.97
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.41
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.00
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.59
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999863594
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.66
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000048073
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.061
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:21.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  90  HammingWeight2, r = 0           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201555979.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27673
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.66
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9911
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.12
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.21
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.73
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.23
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.71
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.62
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1316.90
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7222.73
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 59                 :    0.9918
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.51
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 63                 :    0.9957
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.63
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.86
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.33
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46224
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870224
   j =  1                              :        399907558
   j =  2                              :            46212
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908531
   j =  2                              :            45727
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-6
 p-value of test no 110                :    0.9962
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.63
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.28
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.74
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.25
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.20
 p-value of test no 125                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.24
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.51
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.40
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.51
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17655.97
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.62
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.72
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.55
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.42
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.76
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.53
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.57
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.02
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.72
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.27
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.00
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.06
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.50
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.29
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.05
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.05
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.78
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.18
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.27
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.25
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.83
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.83
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.26
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.68
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.38
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.68
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.36
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.10
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.65
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.10
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.34
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.36
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.06
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.15
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.76
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4293.05
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.40
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12271.92
 p-value of test no 229                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.39
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.35
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000010507
 
 Normal statistic for number of bits   :   0.083
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.92
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999974375
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 241                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 242                :  8.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.64
 p-value of test no 243                :  4.1e-3
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:18.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202637323.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27674
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7134
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.37
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.48
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.90
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.98
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.01
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.32
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  518.90
 p-value of test no 55                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.57
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.13
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.83
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.94
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.34
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.26
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.42
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908048
   j =  2                              :            45970
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908416
   j =  2                              :            45789
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 102                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.75
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.14
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.78
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.93
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.08
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.01
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.80
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.55
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.02
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.18
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.10
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.46
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.60
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.32
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.45
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.59
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.09
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.64
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.59
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.13
 p-value of test no 155                :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.05
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.93
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.01
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.55
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.93
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.25
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.88
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.90
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.61
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.20
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.49
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.75
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.22
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.49
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.26
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.10
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.61
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.19
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.78
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.90
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.26
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.62
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.54
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.59
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.34
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.03
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.73
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.76
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.82
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.70
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.26
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.11
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999933956
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.21
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999940484
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 250                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.17
 p-value of test no 254                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:06.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203718667.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27675
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7141
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.87
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.91
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.57
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.15
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.03
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.44
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.10
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.96
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.35
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6765.67
 p-value of test no 57                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.10
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
 p-value of test no 63                 :    0.9967
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.10
 p-value of test no 65                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.77
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.57
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45573
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908856
   j =  2                              :            45569
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46316
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870316
   j =  1                              :        399907370
   j =  2                              :            46312
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 102                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.19e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.64
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.28
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.37
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.59
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.67
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.90
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.72
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.17
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.11
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.18
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.64
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.59
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.03
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.35
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.21
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.44
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.82
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.34
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.94
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.94
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.01
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.83
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.56
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.71
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.03
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.24
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.60
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.67
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.09
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.84
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.88
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.11
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.83
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.18
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.12
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.39
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.13
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.62
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.70
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.17
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.68
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.18
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.24
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.39
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.03
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.53
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4323.46
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.17
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.32
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.74
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999938828
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.73
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000065521
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:56.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204701707.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27676
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.27
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.15
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.77
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.78
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.92
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.40
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.19
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.59
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   96.14
 p-value of test no 65                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.46
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.09
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46229
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870229
   j =  1                              :        399907545
   j =  2                              :            46223
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46164
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907674
   j =  2                              :            46160
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.17
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.18
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.09
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.11
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.63
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.45
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.90
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.15
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.97
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.65
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.69
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.82
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.97
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.51
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.48
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.44
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.29
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.76
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.94
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.01
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.08
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.48
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.47
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.26
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.64
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.68
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.36
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.46
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.56
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.93
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.04
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.66
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.86
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.87
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.51
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.77
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.55
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.68
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.20
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.59
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9965
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.12
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.25
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.08
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.43
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.46
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.68
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.75
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.58
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.24
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.70
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.49
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.77
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.72
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999825524
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.66
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999897794
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:34.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205750283.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27677
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 9                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.62
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    3.47
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.46
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.95
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.56
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.78
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.82
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.04
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.63
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.57
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.15
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.11
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.70
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.51
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.05
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4862.82
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908446
   j =  2                              :            45771
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908230
   j =  2                              :            45882
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.94
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.83
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.52
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.51
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.39
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.04
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.64
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.10
 p-value of test no 133                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.93
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.81
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17644.19
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.99
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.85
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.09
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.74
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.84
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.44
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.15
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.54
 p-value of test no 157                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.09
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.96
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.52
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.57
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.75
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.01
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.80
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.26
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.90
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.91
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.15
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.13
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.12
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.45
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.16
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.36
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.96
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.04
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.84
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.20
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.86
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.22
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 224                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4671.44
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4321.66
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.81
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.27
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.80
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.07
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000100843
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.25
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999995243
 
 Normal statistic for number of bits   :  -0.038
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:03.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206864395.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27678
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 20                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    3.11
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     666
 p-value of test no 31                 :  4.2e-3
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.05
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.79
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.44
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.43
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.54
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.70
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1302.86
 p-value of test no 56                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7226.15
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.29
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.24
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.02
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.62
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.18
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908182
   j =  2                              :            45903
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908316
   j =  2                              :            45839
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.36
 p-value of test no 117                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.49
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.64
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.45
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.86
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.02
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.17
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.14
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.15
 p-value of test no 136                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.82
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.32
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.43
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.32
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.46
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.47
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.12
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.49
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.62
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.02
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.91
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.99
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.77
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.35
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.00
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.60
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.15
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.88
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.05
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.14
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.68
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.70
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.39
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.83
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.29
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.25
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.28
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.28
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.51
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.65
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.71
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.00
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.07
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.82
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.33
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.13
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.95
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.38
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.20
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.55
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.51
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999976142
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.18
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000134077
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:50.60
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207912971.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27679
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7084
 p-value of test no 20                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.02
 p-value of test no 29                 :  8.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.97
 p-value of test no 30                 :  9.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   26.11
 p-value of test no 46                 :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.24
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.31
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.04
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.88
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.04
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.01
 p-value of test no 53                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.08
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.23
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.92
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.65
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.69
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.85
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.40
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.37
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5299.43
 p-value of test no 68                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908445
   j =  2                              :            45767
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908628
   j =  2                              :            45683
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 108                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.48
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.89
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.21
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.39
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.90
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.27
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.62
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.85
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.62
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.23
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.10
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.23
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.81
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.29
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.87
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.09
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.52
 p-value of test no 152                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.92
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.34
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.32
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.15
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.52
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.95
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.00
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.30
 p-value of test no 160                :    0.9910
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.07
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.74
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.50
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.99
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.43
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.55
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.46
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.38
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.56
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.53
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.03
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.17
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.13
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.00
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.60
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.85
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.77
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.28
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.37
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.75
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.49
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.68
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.48
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.30
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.28
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12067.42
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.73
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.58
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000134443
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.97
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000035857
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9971
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:33.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208928779.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27680
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.41
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.29
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   86.27
 p-value of test no 50                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.43
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.01
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.52
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.65
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.24
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6785.64
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.12
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.52
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.50
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.65
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.55
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46234
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870234
   j =  1                              :        399907534
   j =  2                              :            46230
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908379
   j =  2                              :            45806
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.15
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.13
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.29
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   72.95
 p-value of test no 122                :  3.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.77
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.70
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.65
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17475.97
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.81
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.17
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.91
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.13
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.69
 p-value of test no 152                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.19
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.11
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.14
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.19
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.18
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.73
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.36
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.08
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.15
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.91
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.95
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.38
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.48
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.35
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.46
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.38
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.33
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.74
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.40
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.02
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.49
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.98
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.13
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.13
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.30
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.86
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.13
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.80
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.02
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.67
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.76
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.08
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.34
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.84
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.91
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.38
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999967913
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.48
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999938090
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:46.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189267980.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27681
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.18
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.01
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.22
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.07
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.04
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.25
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.77
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.72
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.65
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.73
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.30
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.05
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.75
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46175
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870175
   j =  1                              :        399907656
   j =  2                              :            46163
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908314
   j =  2                              :            45834
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 93                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-3
 p-value of test no 103                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.67
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.85
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.43
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.31
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.89
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.20
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.39
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.98
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.30
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.06
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17228.44
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.57
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.37
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.75
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.25
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.23
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.71
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.11
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.98
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.70
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.14
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.12
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.37
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.03
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.34
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.99
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.23
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.16
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.51
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.78
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.49
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5227.71
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.05
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.69
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.95
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.40
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.85
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.06
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.18
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.21
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.02
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.90
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.09
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.86
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.68
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.89
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.71
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.13
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.61
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.61
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.91
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000049171
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.02
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999979166
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:47.46
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189923340.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27682
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.09
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.58
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.82
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.38
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.04
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.90
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.04
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.16
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.53
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.68
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.34
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.22
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.25
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.85
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908443
   j =  2                              :            45774
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908042
   j =  2                              :            45979
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.11
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.14
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.93
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.55
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.74
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.96
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.83
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.16
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.01
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.62
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.02
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.00
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.55
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.26
 p-value of test no 151                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.29
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.15
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.30
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.34
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.21
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.94
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.17
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.64
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.93
 p-value of test no 161                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.42
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.81
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.11
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.99
 p-value of test no 165                :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.89
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.34
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.03
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.47
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.71
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.67
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.11
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.98
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.76
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  258.33
 p-value of test no 175                :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.80
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.57
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.56
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.48
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.14
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.43
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 220                :    0.9918
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.54
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.10
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.79
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.41
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.33
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.95
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.15
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999997055
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.19
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999952358
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:08.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190971916.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27683
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 8                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 10                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.09
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.62
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.50
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.60
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.08
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.65
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.50
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.70
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6976.53
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.83
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.23
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.96
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.74
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908439
   j =  2                              :            45770
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46263
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870263
   j =  1                              :        399907475
   j =  2                              :            46261
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 115                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.78
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.88
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.73
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.36
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.81
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.02
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.63
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.24
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.20
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.85
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17409.44
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.41
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.27
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.68
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.44
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.71
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.32
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.50
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.05
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.57
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.39
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.16
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.36
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.89
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.99
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.58
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.60
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.72
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.67
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.14
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.19
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.99
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  445.12
 p-value of test no 169                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.62
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.32
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.31
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.06
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.21
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.9913
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.71
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.75
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.02
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.27
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.59
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.76
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 224                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.27
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.25
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.53
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.74
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.17
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.49
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999887258
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.91
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999988070
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.64
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:32.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192053260.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27684
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.23
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.14
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.23
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.27
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.27
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.36
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.46
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.19
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.05
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.94
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.61
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.36
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4908.93
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908459
   j =  2                              :            45766
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908375
   j =  2                              :            45811
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.87
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.52
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.80
 p-value of test no 122                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.40
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.33
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.92
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.53
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.46
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17691.76
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.48
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.78
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.04
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.92
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.85
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.35
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.46
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.07
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.23
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.08
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.53
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.21
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.78
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.42
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.65
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.98
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.57
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.73
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.56
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.80
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.12
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.77
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.53
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.65
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.92
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.14
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.28
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.24
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    2.18
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.94
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.68
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.99
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.78
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.29
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.93
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.04
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.51
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.64
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.75
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.09
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.11
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000007498
 
 Normal statistic for number of bits   :   0.059
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.57
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000052507
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:55.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193396748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27685
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 11                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1233
 p-value of test no 12                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334353
   j =  1                              :        599997534
   j =  2                              :             1233
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 19                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.39
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.82
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.62
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.77
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.72
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.88
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.40
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7458.53
 p-value of test no 57                 :  3.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.70
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.62
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.56
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.34
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5188.98
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908700
   j =  2                              :            45644
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907831
   j =  2                              :            46080
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.86
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.65
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.77
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.96
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.71
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.23
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.33
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.39
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.13
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.88
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.99
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.04
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.51
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.24
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.01
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.55
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.41
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.71
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.89
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.02
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.48
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.47
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.27
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.01
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.98
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.02
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.50
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.11
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.68
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.70
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.11
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.07
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.10
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.57
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.51
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.70
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.12
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.25
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 185                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 188                :  6.6e-3
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.16
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.00
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.84
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.35
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.50
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.33
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.86
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.78
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.69
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.00
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.68
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000041209
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.30
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999954005
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:30.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9998 
  37  Gap, r = 20                     3.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194609164.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27686
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.93
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.19
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.09
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.55
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.24
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.27
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.13
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.70
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.95
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.03
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.00
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 58                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   53.67
 p-value of test no 61                 :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.30
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.11
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.10
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908222
   j =  2                              :            45883
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908386
   j =  2                              :            45804
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
 p-value of test no 100                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 102                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.43
 p-value of test no 116                :  3.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.28
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.02
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.92
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.44
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.90
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.86
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.25
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.20
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.55
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.79
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.81
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.95
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.77
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.35
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.06
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.36
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.26
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.59
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.42
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.57
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.72
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.98
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.66
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.17
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.91
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.00
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.17
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.06
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.39
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.21
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.81
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.30
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.36
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.56
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.08
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.47
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.00
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.90
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.27
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.66
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.88
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10358.02
 p-value of test no 211                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.49
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.23
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.25
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.53
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.78
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.30
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.42
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.19
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999891677
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.34
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999786812
 
 Normal statistic for number of bits   :   -1.69
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-3
 p-value of test no 251                :    0.9979
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:25.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195461132.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27687
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4482
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.85
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.21
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.37
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.10
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.99
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.56
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.54
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.25
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6697.56
 p-value of test no 57                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.22
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.64
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.04
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.30
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908076
   j =  2                              :            45959
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907665
   j =  2                              :            46160
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.74
 p-value of test no 117                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.40
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.94
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.12
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.21
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.22
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.33
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.51
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.28
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.67
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.09
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.05
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17577.06
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.53
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.58
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.82
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.13
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.84
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.61
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.92
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.16
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.20
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.42
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.12
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.22
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.18
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.47
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.43
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.78
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.42
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.89
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.06
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4820.91
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.53
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.19
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.70
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.07
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.05
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.56
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.53
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.94
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.36
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.07
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.73
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.56
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.84
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.86
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.70
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4649.64
 p-value of test no 222                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.26
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.64
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.47
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.03
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.51
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.56
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999937001
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.81
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999998273
 
 Normal statistic for number of bits   :  -0.014
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    2.21
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:11.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196444172.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27688
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5528
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.22
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.87
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.00
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.08
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.63
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.02
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.98
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.62
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7189.92
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.67
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.79
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.10
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.27
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908130
   j =  2                              :            45932
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908229
   j =  2                              :            45884
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 104                :    0.9917
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.74
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.69
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.10
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.28
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.25
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.31
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.21
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.90
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.76
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.33
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.87
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.70
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.59
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.62
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.26
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.82
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.39
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.59
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.16
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.44
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.58
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.60
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.46
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.92
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.48
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.85
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.49
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.18
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.08
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.42
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.06
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.19
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.88
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.28
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.98
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.49
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.70
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.57
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.35
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.56
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.80
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.71
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.95
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.59
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.64
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4718.17
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.00
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.35
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.61
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.62
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.94
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.57
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000148147
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.87
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999856757
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:37.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197754892.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27689
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7112
 p-value of test no 18                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.34
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.82
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.35
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.80
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.73
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.57
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1329.56
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.90
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.71
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.26
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.77
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.40
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908195
   j =  2                              :            45901
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908230
   j =  2                              :            45879
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-4
 p-value of test no 110                :  2.2e-4    *****
 
 Anderson-Darling statistic = A2       :    5.17
 p-value of test no 111                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.11
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.18
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.21
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.81
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.90
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.61
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.32
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.52
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.87
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17630.93
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.96
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.80
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.24
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.86
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.94
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.49
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.14
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.16
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.15
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.36
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.68
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.85
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.97
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.09
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.88
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.79
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.90
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.82
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.41
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.36
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.74
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.97
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.65
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.00
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.87
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.56
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.61
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.64
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.22
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.51
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.90
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.61
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.97
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.59
 p-value of test no 217                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.75
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.15
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.37
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.00
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.40
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.97
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.82
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999930590
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.16
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000000607
 
 Normal statistic for number of bits   : 4.80e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:36.42
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198705164.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27690
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5285
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.61
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.26
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.85
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.59
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.08
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.01
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.57
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.41
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.06
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.72
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.45
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.46
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.94
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.40
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4905.48
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46225
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870225
   j =  1                              :        399907552
   j =  2                              :            46221
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908538
   j =  2                              :            45722
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.11
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.13
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.88
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.85
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.73
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.69
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.37
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.22
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.00
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.93
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.41
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.44
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.18
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.56
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.85
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.59
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.24
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.17
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.34
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.35
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.71
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.62
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.73
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.90
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.28
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.81
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.13
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.18
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.99
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.77
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.51
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.20
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.98
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.70
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.37
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.93
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.52
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.50
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.39
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.02
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.88
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.08
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.29
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.85
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.48
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.61
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.15
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.44
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3932.39
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.52
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.84
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.20
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000221359
 
 Normal statistic for number of bits   :    1.75
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.65
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999948425
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 235                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 237                :  6.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.45
 p-value of test no 238                :    0.9928
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:03.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199884812.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27691
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    3.09
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     262
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.31
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.44
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.77
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.04
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.77
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.60
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.13
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.85
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.67
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.40
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.29
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908806
   j =  2                              :            45591
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908381
   j =  2                              :            45802
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.21e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.17
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.06
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.66
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.35
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.05
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.73
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.34
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.33
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.18
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.57
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17527.38
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.30
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.02
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.05
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.96
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.15
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.33
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.83
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.21
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.88
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.08
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.22
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.44
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.59
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.98
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.58
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.08
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.92
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.41
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.81
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.46
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.14
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.91
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.06
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.80
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.78
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.13
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.69
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.88
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.92
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.35
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.46
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.91
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.30
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5042.38
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.98
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.69
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.46
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.74
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.82
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.29
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000017338
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000084634
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:07.61
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201097228.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27692
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 3                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 10                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.23
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.91
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.37
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.07
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.61
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.57
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.03
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6945.89
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.06
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.35
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.63
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   85.35
 p-value of test no 67                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.03
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907657
   j =  2                              :            46170
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908440
   j =  2                              :            45774
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-3
 p-value of test no 80                 :    0.9986
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 86                 :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-5
 p-value of test no 103                : 1 -  1.1e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.14
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.16
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.39
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.65
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.29
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.71
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.33
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17262.49
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.74
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.16
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.31
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.68
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.78
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.38
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.51
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.57
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.26
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.33
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.24
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.57
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.74
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.75
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.36
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.53
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.63
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.35
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.39
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5207.10
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.08
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.73
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.04
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.18
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5211.77
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.53
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.24
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.13
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.79
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.59
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.12
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 212                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10273.01
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.85
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.28
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.64
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.80
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.58
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12169.86
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.62
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999941609
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.31
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000000823
 
 Normal statistic for number of bits   : 6.51e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:01.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201981964.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27693
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4213
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.80
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.93
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.34
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.01
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.77
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.22
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.00
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.74
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.08
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.32
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.92
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.84
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.78
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4958.12
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46099
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870099
   j =  1                              :        399907805
   j =  2                              :            46093
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908295
   j =  2                              :            45845
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 101                :    0.9930
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.86
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.86
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.95
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.46
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.32
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.92
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.28
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.10
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.47
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.73
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.67
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.20
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17647.19
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.06
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.27
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.17
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.48
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.14
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.11
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.45
 p-value of test no 154                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.53
 p-value of test no 155                :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.53
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.27
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.47
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.36
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.69
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.52
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.43
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.50
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.64
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.39
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.00
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.33
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.98
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.27
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.07
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.25
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.75
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.92
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.63
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.83
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.17
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.96
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.48
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
 p-value of test no 205                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.46
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9673.25
 p-value of test no 211                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.76
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.63
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.22
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.35
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.92
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.54
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.48
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.68
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000029863
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.96
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999929468
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:48.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202997772.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27694
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 6                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9955
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.75
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.27
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.22
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.32
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.53
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.48
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.97
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.41
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.72
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.77
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6872.82
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.37
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 63                 :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    6.03
 p-value of test no 64                 :  1.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   96.54
 p-value of test no 65                 :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.49
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5223.66
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908648
   j =  2                              :            45667
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908024
   j =  2                              :            45982
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-6
 p-value of test no 109                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.47e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.89e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.72
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.74
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.48
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.86
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.21
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.68
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.21
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.85
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.52
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.97
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17714.40
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.18
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.99
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.21
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.13
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.47
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.83
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.18
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.63
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.38
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   91.27
 p-value of test no 159                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.07
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.79
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.88
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.24
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.89
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.25
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.62
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.35
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.26
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.12
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.76
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.34
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.91
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.91
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.35
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    2.72
 p-value of test no 189                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-4
 p-value of test no 193                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.02
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.40
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.63
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.45
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.32
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.62
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.74
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.69
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.66
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11630.23
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.57
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000036844
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.74
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000228376
 
 Normal statistic for number of bits   :    1.81
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:35.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204144652.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27695
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4172
 p-value of test no 14                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.45
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.07
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.11
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.16
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.69
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.22
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.72
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.12
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.89
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.96
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.11
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.54
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.09
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.97
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.30
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908218
   j =  2                              :            45888
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908641
   j =  2                              :            45672
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 94                 :  2.7e-3
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 95                 :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  4.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.03
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.97
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.25
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.27
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.91
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.17
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.79
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.84
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.02
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17660.74
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.78
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.22
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.85
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.88
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.70
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.14
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.23
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.37
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.85
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.47
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.03
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.52
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.48
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.77
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.82
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.87
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.33
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.22
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.59
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.86
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.14
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.21
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.98
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.60
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.33
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.45
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.09
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.99
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.84
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.45
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.38
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.93
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.16
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.33
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.77
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.61
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.31
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.73
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.65
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.09
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000161173
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.82
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999958706
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:02.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205586444.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27696
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.25
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.56
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.40
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.17
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.69
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.85
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.41
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.93
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.96
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.82
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.16
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.27
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.84
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.63
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4896.58
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45490
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869490
   j =  1                              :        399909023
   j =  2                              :            45484
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907976
   j =  2                              :            46009
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.05e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.98
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.84
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.26
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.34
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.60
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.11
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.78
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.47
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17212.28
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.05
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.33
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.40
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.34
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.57
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.75
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.38
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.15
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.29
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.04
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.17
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.15
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.86
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.65
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.93
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.88
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.61
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.31
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.09
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.76
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.14
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.06
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.51
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.28
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.14
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.37
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.36
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.55
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 185                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.65
 p-value of test no 188                :  4.0e-3
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9964
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.50
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.08
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10174.51
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.41
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.38
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 223                :  6.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 225                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4620.69
 p-value of test no 226                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.42
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.08
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.91
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12169.20
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.25
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999970421
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.88
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000004486
 
 Normal statistic for number of bits   :   0.035
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 236                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 237                :  6.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    2.84
 p-value of test no 239                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.078
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206635020.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27697
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.84
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.74
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.51
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.81
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  172.70
 p-value of test no 54                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.58
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.11
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6756.99
 p-value of test no 57                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.32
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.71
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.18
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.86
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4908.88
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907779
   j =  2                              :            46106
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908190
   j =  2                              :            45899
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.52
 p-value of test no 115                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.57
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.86
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.79
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.76
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   69.64
 p-value of test no 123                :  9.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.87
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.43
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.64
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.35
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.76
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17243.32
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.63
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.94
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.18
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.83
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.69
 p-value of test no 150                :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.59
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.47
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.30
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.70
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.43
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.38
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.89
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.00
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.08
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.81
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.10
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.65
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.77
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.22
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.42
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.16
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.73
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.84
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.81
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.70
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.25
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.06
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.74
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  292.76
 p-value of test no 174                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.00
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 185                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.11
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.36
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.98
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.32
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.59
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.75
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 221                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5147.33
 p-value of test no 222                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.28
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.63
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.35
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.62
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.95
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.58
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000177193
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.02
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999923660
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.062
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:29.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           9.3e-4
  79  RandomWalk1 R (L=10000, r=15)   0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207683596.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27698
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.39
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.02
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.06
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.88
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.40
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.31
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.82
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.42
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.39
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.90
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.23
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.15
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.76
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.87
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.86
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.47
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908001
   j =  2                              :            45992
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908133
   j =  2                              :            45932
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.88
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.23
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.96
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.38
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.30
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.81
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.18
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.33
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.06
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17540.76
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.70
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.76
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.15
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.43
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.56
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.10
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.21
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.11
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.82
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.50
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.89
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.28
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  115.04
 p-value of test no 160                :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.54
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.38
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.39
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.05
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.15
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.37
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.66
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.43
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.86
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.67
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.19
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.51
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.58
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.81
 p-value of test no 174                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.40
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.01
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.16
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.95
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.27
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.54
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.73
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.79
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.52
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3942.92
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.16
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.10
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.80
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.30
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000084067
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.79
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999979385
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:52.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208699404.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27699
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.34
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.63
 p-value of test no 34                 :  4.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    3.07
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.80
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.38
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.88
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.84
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.13
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.72
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.13
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7157.36
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.69
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.22
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.84
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.28
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908229
   j =  2                              :            45881
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.43
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.82
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.95
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.28
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.66
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.82
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.83
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.33
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.43
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.62
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.93
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.24
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.91
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.53
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.75
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.55
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.63
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.12
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.01
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.93
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.09
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.41
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.03
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.98
 p-value of test no 160                :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.48
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.02
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.02
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.04
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.98
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.26
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.21
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5294.38
 p-value of test no 168                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.74
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.42
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.02
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.17
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.46
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.39
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.43
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.15
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.47
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.02
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10243.41
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.25
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.91
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.70
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.61
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.70
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.81
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.41
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.92
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000299470
 
 Normal statistic for number of bits   :    2.37
 p-value of test no 232                :  9.0e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.84
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000026743
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:56:05.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209780748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27700
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 12                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7110
 p-value of test no 19                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    3.50
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9978
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.09
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.30
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.12
 p-value of test no 51                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.31
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.66
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.09
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.67
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7236.81
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.02
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.84
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.41
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.30
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908317
   j =  2                              :            45840
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908585
   j =  2                              :            45703
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.90
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.42
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.57
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.31
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.90
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.37
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.17
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.97
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.38
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17351.79
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.90
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.92
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.45
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.28
 p-value of test no 149                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.73
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.70
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.61
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.65
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.06
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.32
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.28
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.68
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.77
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.92
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.31
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.68
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.67
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.19
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.04
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.82
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.44
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.56
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.69
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.01
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.70
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.88
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.16
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.64
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.71
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.09
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.93
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.17
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.59
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.92
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.42
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3928.64
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.54
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.81
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.94
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.27
 p-value of test no 231                :  5.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999783701
 
 Normal statistic for number of bits   :   -1.71
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999893264
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:23:55.31
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189300749.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27701
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     824
 p-value of test no 25                 :    0.9946
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    3.95
 p-value of test no 44                 :  9.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.95
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.87
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.35
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.64
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.75
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.85
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.47
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.72
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  512.42
 p-value of test no 55                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.09
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6686.01
 p-value of test no 57                 :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.10
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.06
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.66
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.69
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908085
   j =  2                              :            45950
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907983
   j =  2                              :            46004
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 101                :  7.3e-4    *****
 
 Anderson-Darling statistic = A2       :    7.11
 p-value of test no 102                :  3.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.76
 p-value of test no 115                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.36
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.63
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.44
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.42
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.51
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.83
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.62
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.05
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.15
 p-value of test no 137                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.88
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.55
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.53
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.65
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.84
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.28
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.87
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.95
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.45
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.90
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.97
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.87
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.11
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.26
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.45
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.09
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.81
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.92
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.23
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.84
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.38
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.14
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.64
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.07
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.68
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.49
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.71
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.30
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.76
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.34
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.80
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.12
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.15
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.47
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.00
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.73
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.86
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.31
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.47
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.98
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.78
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000058360
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.82
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000054877
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:23.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               3.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190939149.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27702
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5540
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    5.53
 p-value of test no 39                 :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.28
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.42
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.02
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.23
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.18
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.92
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.29
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.78
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.89
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.30
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.09
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.33
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46143
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870143
   j =  1                              :        399907719
   j =  2                              :            46133
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908263
   j =  2                              :            45861
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 118                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.22
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.61
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.42
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.98
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.08
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.22
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.67
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.26
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.28
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.29
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.65
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.31
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.42
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.38
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.68
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.53
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.97
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.66
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.61
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.53
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.45
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.38
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.54
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.06
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.54
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.09
 p-value of test no 166                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.71
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.61
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.00
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.91
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.98
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.07
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.09
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.98
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.35
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.49
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.01
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.20
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.88
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.61
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.53
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.85
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.81
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.86
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3858.56
 p-value of test no 227                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.20
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.92
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.12
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.96
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000039586
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.63
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000156022
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.88
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:23.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191987725.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27703
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    8.38
 p-value of test no 34                 :  8.4e-5    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.62
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.48
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.64
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.31
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.88
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.32
 p-value of test no 53                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.99
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.89
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1600.12
 p-value of test no 56                 :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.23
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.48
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.14
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.36
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.38
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.67
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908211
   j =  2                              :            45887
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45681
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869681
   j =  1                              :        399908641
   j =  2                              :            45675
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 76                 :  7.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    5.19
 p-value of test no 78                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.03
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.34
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.74
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 127                :    0.9945
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 128                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.92
 p-value of test no 129                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.21
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.12
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.63
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.28
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 144                :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.91
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.06
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.20
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.67
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.39
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.64
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.94
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.61
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.97
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.05
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.99
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.81
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.32
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.93
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.85
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.40
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.76
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.61
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.13
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.99
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.13
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.64
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  443.97
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.47
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.54
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.44
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.83
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.02
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.68
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.23
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.18
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.15
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.22
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.99
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.03
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.83
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.51
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.11
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.17
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11570.63
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12080.90
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.84
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000044767
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.26
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000104251
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:44.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            8.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193036301.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27704
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 9                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7083
 p-value of test no 21                 :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    3.65
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.85
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.32
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.20
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.49
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.52
 p-value of test no 51                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.76
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.14
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.53
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.40
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.95
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.99
 p-value of test no 61                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.53
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.27
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.79
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908996
   j =  2                              :            45496
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908205
   j =  2                              :            45896
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.90
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.12
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.28
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.19
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.53
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.97
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.56
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.67
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.79
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.61
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.34
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.25
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.60
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.92
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.93
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.30
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.76
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.86
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.26
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.12
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.88
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.35
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.85
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.53
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.31
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.56
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.98
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.67
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.32
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.92
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.81
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.16
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.64
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  295.08
 p-value of test no 174                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.60
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.68
 p-value of test no 176                :    0.9974
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.99
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.95
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.96
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.62
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.56
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.89
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.31
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.18
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.17
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.35
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.54
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000016042
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.54
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000106588
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    2.91
 p-value of test no 254                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:16.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194084877.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27705
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.22
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.73
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.88
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.46
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.28
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.94
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.73
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.53
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.17
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.24
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.89
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.30
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908482
   j =  2                              :            45756
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908251
   j =  2                              :            45870
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 92                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.7e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-4
 p-value of test no 112                :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.66
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.93
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.23
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.08
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.26
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.05
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.99
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.41
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.72
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.34
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.71
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.13
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.75
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.67
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.98
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.01
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.70
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.62
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.59
 p-value of test no 157                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.76
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.72
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.67
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.11
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.53
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.17
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.18
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.97
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.71
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.49
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.58
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  447.35
 p-value of test no 169                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.84
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.11
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.75
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.57
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.66
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.42
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
 p-value of test no 200                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.74
 p-value of test no 203                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.55
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.86
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.57
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.13
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.99
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.72
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.86
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.84
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.85
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.90
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000006694
 
 Normal statistic for number of bits   :   0.053
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.76
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999918788
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    2.87
 p-value of test no 249                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:25.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195133453.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27706
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.77
 p-value of test no 47                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.02
 p-value of test no 48                 :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.08
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.34
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.60
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.27
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.09
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.86
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.66
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.08
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.90
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.31
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.60
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.47
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.68
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.07
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908138
   j =  2                              :            45928
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907817
   j =  2                              :            46084
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.84
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.53
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.88
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.56
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.74
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.13
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.75
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.76
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.34
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17349.32
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.57
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.92
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.17
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.90
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.52
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.65
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.80
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.15
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.37
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.99
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.39
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.01
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.37
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.32
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.27
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.17
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.03
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.56
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.65
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.61
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.69
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.77
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.90
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.83
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.98
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.56
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.31
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.00
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.75
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.05
 p-value of test no 198                :    0.9979
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.86
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.20
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.75
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.65
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.34
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 223                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 225                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4657.07
 p-value of test no 226                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.81
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.99
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.66
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.74
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.98
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000135820
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.61
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000042301
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196083725.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27707
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7082
 p-value of test no 21                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.9915
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     659
 p-value of test no 31                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.43
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.40
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.48
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.92
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.46
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.46
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.47
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.27
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.05
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.91
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.47
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.51
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.29
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.34
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908195
   j =  2                              :            45898
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907865
   j =  2                              :            46066
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.08
 p-value of test no 117                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.92
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.45
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.25
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.05
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.33
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.67
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.68
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.03
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.05
 p-value of test no 133                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.24
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.33
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.82
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.61
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.80
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.55
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.69
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.79
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.11
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.07
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.42
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.82
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.37
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.54
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.33
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.23
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.07
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.64
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.35
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.72
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.26
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.77
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  309.32
 p-value of test no 169                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.63
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.17
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.47
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.74
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.29
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.97
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.33
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.65
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.99
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.65
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.95
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.74
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.28
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4387.06
 p-value of test no 227                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.08
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.55
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.43
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.49
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000108259
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.58
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000008728
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    2.23
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:49.31
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197099533.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27708
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 3                  :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 12                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.92
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.24
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.91
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.37
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.26
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.33
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.32
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.81
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.77
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.10
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.02
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.06
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.14
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908177
   j =  2                              :            45910
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907898
   j =  2                              :            46048
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.73
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.65
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.94
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.92
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.22
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.20
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.00
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.22
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.40
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.55
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.35
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.02
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.56
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.96
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.92
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.55
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.78
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.15
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.67
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.01
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.39
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.62
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.52
 p-value of test no 159                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.97
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.45
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.90
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.34
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.83
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.48
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.83
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.94
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.66
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.12
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.40
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.62
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.63
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.26
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.11
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.27
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.72
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.38
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.19
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.86
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.97
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.48
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.64
 p-value of test no 217                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.28
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.29
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.63
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.30
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.74
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.54
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.48
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999998201
 
 Normal statistic for number of bits   :  -0.014
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.24
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000146674
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9913
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.056
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:44.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198246413.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27709
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1232
 p-value of test no 11                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334352
   j =  1                              :        599997536
   j =  2                              :             1232
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.10
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.08
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.30
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.27
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.67
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  277.34
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.83
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1347.66
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.10
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.11
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.09
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.82
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.51
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907840
   j =  2                              :            46077
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908365
   j =  2                              :            45816
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.17
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.55
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.84
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.85
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.20
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.83
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.36
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.96
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.04
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.88
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.13
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.43
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.40
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.83
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.69
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.38
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.37
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.10
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.00
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.23
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.26
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.63
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.51
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.84
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.07
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.23
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.66
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.99
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.49
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.38
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.83
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.67
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.84
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.12
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.87
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.69
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.26
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.62
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 205                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    7.28
 p-value of test no 206                :  2.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  276.39
 p-value of test no 207                :  2.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.94
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.37
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.59
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.71
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.15
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.89
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.52
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.60
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.82
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000003526
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   95.50
 p-value of test no 233                :  4.3e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999922184
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:06.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9999 
  89  PeriodsInStrings, r = 20        2.8e-4
  102  Run of bits, r = 27             4.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199163917.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27710
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.42
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.52
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.56
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.02
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.34
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.09
 p-value of test no 52                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.38
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.88
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.15
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.01
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.46
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.79
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.00
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.23
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.46
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908410
   j =  2                              :            45792
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45530
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869530
   j =  1                              :        399908943
   j =  2                              :            45524
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.20
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.46
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.25
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.79
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.13
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.87
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.98
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.15
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.27
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.19
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.02
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.56
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.00
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.55
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.10
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.88
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.03
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.60
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.02
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.59
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.98
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.34
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.56
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.71
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.08
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.98
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.32
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.22
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.35
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.60
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.08
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.73
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.57
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.97
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.05
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.11
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.02
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.49
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.50
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.97
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.94
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.40
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.49
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9754.07
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.70
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.28
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.68
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.43
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.75
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.22
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.72
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000081352
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.28
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999930668
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:07.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200146957.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27711
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.42
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.09
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.47
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.78
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.44
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.68
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.62
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.45
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.73
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7289.76
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.23
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.21
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.58
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.03
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.14
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908503
   j =  2                              :            45747
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908160
   j =  2                              :            45917
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.95
 p-value of test no 118                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.86
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.93
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.71
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.72
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.34
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.44
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.27
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.44
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.92
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17803.12
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.77
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.60
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.98
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.02
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.57
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.47
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.51
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.24
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.55
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.26
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.53
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.00
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.49
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.15
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.76
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.94
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.93
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.74
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.83
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.04
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.65
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.15
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.99
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.95
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.90
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.39
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.79
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.89
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.77
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.90
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    2.26
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.89
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.54
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.28
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.09
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.82
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.97
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.56
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.72
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.61
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.84
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.21
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.92
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999986525
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.68
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999934454
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:05.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201162765.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27712
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9925
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.26
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.65
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.89
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.03
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.70
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.13
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.34
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.46
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.28
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.86
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.54
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.51
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4876.29
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908115
   j =  2                              :            45938
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908206
   j =  2                              :            45894
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 92                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 116                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.82
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.08
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.27
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.90
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.30
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.48
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.94
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.75
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.61
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.33
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.97
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.63
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.88
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.87
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.94
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.40
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.04
 p-value of test no 152                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.52
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.10
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.46
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  201.51
 p-value of test no 156                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.43
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.08
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.20
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.57
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.85
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.30
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.42
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.76
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.47
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.74
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.23
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.89
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.23
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.67
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.38
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.82
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.80
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.66
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.37
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.03
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.46
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.05
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.65
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.00
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.13
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.98
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.85
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.01
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.50
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.32
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000093196
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.12
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000090085
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:35.76
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202014733.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27713
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 4                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    3.06
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     255
 p-value of test no 37                 :    0.9957
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.58
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.07
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.95
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.72
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.12
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.09
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.81
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.57
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.51
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.67
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.58
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908401
   j =  2                              :            45792
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908582
   j =  2                              :            45706
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.20
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.87
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.12
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.79
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.54
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.18
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.30
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.11
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.03
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.15
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.89
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.51
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.88
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.40
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.36
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.87
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.76
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.17
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.96
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.83
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.54
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.70
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.63
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.15
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.12
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.36
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.67
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.24
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.48
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.13
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.80
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.33
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.10
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.52
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.21
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.51
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.01
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.48
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.79
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.14
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.99
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.99
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.42
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.58
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.98
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.14
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.97
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.13
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.68
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999989732
 
 Normal statistic for number of bits   :  -0.081
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.30
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999969749
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:03.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203030541.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27714
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 9                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     256
 p-value of test no 37                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.56
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.01
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.53
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.79
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.81
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.13
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1542.64
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6913.89
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.88
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.56
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.99
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.97
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908504
   j =  2                              :            45745
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908408
   j =  2                              :            45790
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
 p-value of test no 76                 :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.19
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.34
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.13
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.35
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.11
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.83
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 139                :  3.8e-3
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.86
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.56
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.47
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.22
 p-value of test no 147                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.50
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.80
 p-value of test no 150                :    0.9945
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.17
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.26
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.10
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.70
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.62
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.72
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.63
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.22
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.77
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.93
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.05
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.58
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.98
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.60
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.55
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.67
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.72
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.77
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.54
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.81
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.84
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.73
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.88
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
 p-value of test no 181                :    0.9980
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 183                :    0.9911
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.63
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.37
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.93
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.22
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.24
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.90
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.85
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.12
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.40
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.63
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.21
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999973637
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.28
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000027340
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:26.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204013581.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27715
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 15                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7535
 p-value of test no 18                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    4.90
 p-value of test no 36                 :  3.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.76
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.17
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.25
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.93
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.10
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.66
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.83
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.30
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.21
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.83
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.54
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.26
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.67
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.88
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908394
   j =  2                              :            45800
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908262
   j =  2                              :            45866
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.38
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.36
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.52
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.59
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.97
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.02
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.55
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.60
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.76
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.68
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.55
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.72
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.72
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.24
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.98
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.65
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.39
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.74
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.64
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.19
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.77
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.41
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.51
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.62
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.33
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.56
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.45
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.25
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.54
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.18
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.89
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.07
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.81
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.48
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.83
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.11
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    2.38
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.05
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.54
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.69
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.12
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.80
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.95
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.25
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.95
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.54
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.19
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.50
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.43
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999973139
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.88
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999995582
 
 Normal statistic for number of bits   :  -0.035
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    2.09
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:15.85
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205094925.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27716
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1484
 p-value of test no 10                 :  7.2e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334604
   j =  1                              :        599997032
   j =  2                              :             1484
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 12                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.80
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.95
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.53
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.05
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.51
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  368.42
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.28
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.16
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.11
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.86
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.11
 p-value of test no 66                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.02
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4892.96
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908618
   j =  2                              :            45685
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908236
   j =  2                              :            45879
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9905
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.43
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.64
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.23
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.68
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.53
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.93
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.65
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.15
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.29
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.08
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.55
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.65
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.90
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.51
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.92
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.28
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.93
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.73
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.14
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.82
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.74
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.72
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.06
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.58
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.86
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.44
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.76
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.64
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.48
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.47
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.84
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.62
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.20
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.55
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.28
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.60
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.93
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.29
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.10
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.80
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.77
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.71
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.36
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9812.20
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.25
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.83
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.40
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4270.38
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.04
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.77
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11547.59
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.38
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999887174
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.65
 p-value of test no 233                :    0.9935
 
 
 -----------------------------------------------
 Total number of bits:  8000038629
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:51.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206077965.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27717
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997301
   j =  2                              :             1348
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7507
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 32                 :    0.9991    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.25
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.43
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.25
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.09
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.22
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.97
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.75
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.22
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.42
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.77
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.63
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.92
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.14
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908473
   j =  2                              :            45759
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908931
   j =  2                              :            45524
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-6
 p-value of test no 109                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.94
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.93
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.73
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.57
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.71
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.73
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.22
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.55
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.13
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.61
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.66
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17235.16
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.05
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.59
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.54
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.25
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.90
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.56
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.84
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.50
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.25
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.52
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.38
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.34
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.30
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.33
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.93
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.63
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.49
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.86
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.57
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.69
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.37
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.45
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.64
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.25
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.33
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.38
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.93
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.15
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.90
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    2.09
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.72
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.99
 p-value of test no 207                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.96
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9766.17
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.18
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.82
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.65
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.62
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.44
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.41
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.95
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000058105
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.82
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999994802
 
 Normal statistic for number of bits   :  -0.041
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 241                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.13
 p-value of test no 244                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:14.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207126541.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27718
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.62
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.67
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.32
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.26
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.45
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.52
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.38
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.56
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.72
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.72
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.50
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.32
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4892.36
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46222
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870222
   j =  1                              :        399907557
   j =  2                              :            46220
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908323
   j =  2                              :            45834
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.43
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.59
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.56
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.22
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.59
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.70
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.28
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.23
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.10
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17197.84
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.55
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.75
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.79
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.44
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.97
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.28
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.08
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.84
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.29
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.75
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.42
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.86
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.29
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.72
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.71
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.47
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.74
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.98
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.91
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.68
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.22
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.47
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.20
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.24
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.59
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.15
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.14
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.58
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.58
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.17
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.00
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.67
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10382.31
 p-value of test no 211                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.56
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.66
 p-value of test no 217                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.03
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.82
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.75
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.74
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.88
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.26
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.09
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999849653
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.10
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000048478
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    3.06
 p-value of test no 244                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:38.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208109581.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27719
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.89
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    4.84
 p-value of test no 45                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.53
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.89
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.03
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.17
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.75
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.42
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.31
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.66
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.39
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.48
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.48
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.84
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.96
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.97
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908390
   j =  2                              :            45802
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908093
   j =  2                              :            45949
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.41
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.09
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.12
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.23
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.77
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.23
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.29
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.12
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17190.86
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.50
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.87
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.33
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.06
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.50
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.29
 p-value of test no 153                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.40
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.57
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.73
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.88
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.08
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.48
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.32
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.57
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.82
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.73
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.60
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.19
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.63
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.65
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.41
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.78
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.17
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.94
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.09
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.60
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.66
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.44
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.79
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.71
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.57
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.60
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.00
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.27
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 216                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.87
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.70
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3894.52
 p-value of test no 227                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.65
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.15
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.45
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.89
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999818501
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.50
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999855218
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.021
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    2.32
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:19.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209158157.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27720
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7086
 p-value of test no 18                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.75
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.13
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.15
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.29
 p-value of test no 53                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.15
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.34
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.89
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.17
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   51.55
 p-value of test no 61                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.40
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.67
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.52
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908137
   j =  2                              :            45924
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908170
   j =  2                              :            45909
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.24
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.64
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.44
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.89
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.58
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.92
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.46
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.81
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.70
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.81
 p-value of test no 146                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.08
 p-value of test no 147                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.17
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.27
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.01
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.77
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.96
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.44
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.13
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.79
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.10
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.59
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.07
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.17
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.91
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.40
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.63
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.95
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.46
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.35
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.17
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.68
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.59
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.19
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.37
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.48
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.17
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.45
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.03
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.82
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.21
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.48
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.18
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.96
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.26
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.43
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.22
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.71
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.62
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000031549
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.84
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000099589
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:20.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189333518.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27721
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 12                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.15
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.90
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.80
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.52
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.11
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.79
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.50
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.81
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.33
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.55
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.28
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.65
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.73
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.44
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.31
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5240.64
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908441
   j =  2                              :            45778
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908371
   j =  2                              :            45807
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.61
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.53
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.06
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.91
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.13
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.98
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 130                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.92
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.60
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.49
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.22
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.51
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.62
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.39
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.10
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.25
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.21
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.72
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.76
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.05
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.75
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.71
 p-value of test no 158                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.29
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.59
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.43
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.74
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.05
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.43
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.73
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.80
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.15
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.26
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.06
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.01
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.43
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.34
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.99
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.07
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.09
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.64
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.11
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 204                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 205                :  7.0e-4    *****
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 206                :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  254.66
 p-value of test no 207                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.45
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.19
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 218                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.39
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.25
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.29
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.85
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.59
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11580.28
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.04
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000144748
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.48
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999980315
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:46.11
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190021646.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27722
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.97
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.74
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.79
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.41
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.28
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.40
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.15
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.44
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.27
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.99
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.70
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.01
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.20
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46231
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870231
   j =  1                              :        399907543
   j =  2                              :            46221
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908345
   j =  2                              :            45817
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 83                 :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.60
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.71
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.30
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.90
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.90
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.10
 p-value of test no 134                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.45
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17622.91
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.39
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.46
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.56
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.35
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.10
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.49
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.89
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.85
 p-value of test no 156                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.17
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.87
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.56
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.92
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.08
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.71
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.87
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.49
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.53
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.21
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.70
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.86
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.23
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.43
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.40
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.56
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.29
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.44
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  149.13
 p-value of test no 175                :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.56
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.27
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.87
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.49
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.43
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.22
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.96
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.64e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.62
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.53
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.78
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.48
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.62
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.06
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.17
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999949220
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.63
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000055798
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    2.20
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:37.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191168526.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27723
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.57
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    6.97
 p-value of test no 42                 :  3.5e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.61
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.30
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.81
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.11
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.94
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.85
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.33
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.75
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.42
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.39
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.70
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45497
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869497
   j =  1                              :        399909012
   j =  2                              :            45485
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45510
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869510
   j =  1                              :        399908983
   j =  2                              :            45504
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.59
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.30
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.56
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.35
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.56
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.71
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.14
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.80
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.67
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.13
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.97
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.61
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.64
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.28
 p-value of test no 148                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.74
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.10
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.88
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.25
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.50
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.82
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.05
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.99
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.41
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.28
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.40
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.18
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.41
 p-value of test no 165                :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.99
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.98
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4808.66
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.21
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.80
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.29
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.94
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.11
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.52
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.08
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.89
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.89
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.48
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.83
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.08
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.19
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.65
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.26
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.23
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.95
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.77
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12211.95
 p-value of test no 229                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.47
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.32
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999931181
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.43
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000144655
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:11.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192577550.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27724
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4493
 p-value of test no 17                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9902
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.02
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.22
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.04
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.52
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.66
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.38
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.32
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.77
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.77
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7276.20
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.84
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.56
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.57
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.24
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908634
   j =  2                              :            45680
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908207
   j =  2                              :            45892
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-5
 p-value of test no 113                :    0.9921
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.84
 p-value of test no 115                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.39
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.22
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.40
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.57
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.26
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.26
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.19
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.88
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.89
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.24
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.63
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.55
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.41
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.15
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.21
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.29
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.10
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.81
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.70
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  120.85
 p-value of test no 160                :  4.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.06
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.93
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.34
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.04
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.79
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.91
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.31
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.01
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.24
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.62
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.39
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.86
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.96
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.45
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.45
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.71
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.64
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    2.95
 p-value of test no 184                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.19
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.30
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.74
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.63
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.48
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.10
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.58
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.29
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.55
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.18
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.97
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.95
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.29
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999950657
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.83
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999871211
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 237                :  2.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.06
 p-value of test no 238                :    0.9989
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:20.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193462286.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27725
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 10                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.12
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.47
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.15
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.02
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.63
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.73
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.92
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.16
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  510.94
 p-value of test no 55                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.73
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6987.15
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.26
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   91.76
 p-value of test no 65                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.82
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.82
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45636
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908730
   j =  2                              :            45632
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46434
 p-value of test no 71                 :  4.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870434
   j =  1                              :        399907137
   j =  2                              :            46424
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 92                 :    0.9980
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.38
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.22
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.78
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.27
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.42
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.65
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.44
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17554.00
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.01
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.75
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.99
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.98
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.70
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.12
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.30
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.13
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.80
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.06
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.45
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.99
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.47
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.11
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.22
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.93
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.33
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.00
 p-value of test no 165                :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.07
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.78
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.00
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.64
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.81
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.26
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.64
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.00
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.99
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.57
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.38
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.74
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.45
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.08
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.50
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.01
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.71
 p-value of test no 216                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.79
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.72
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.73
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.09
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.73
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.24
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.19
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999992132
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.53
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000012412
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:59.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194314254.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27726
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.73
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.83
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.09
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.38
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.57
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.84
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.59
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.11
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.38
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.09
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.17
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.62
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.09
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.89
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.20
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.62
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908607
   j =  2                              :            45680
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908520
   j =  2                              :            45731
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.26
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.79
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.17
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.42
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.71
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.37
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.71
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.07
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.66
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.85
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.16
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.59
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.91
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.81
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.53
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.75
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.64
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.32
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.99
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.98
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.75
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.56
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.50
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.80
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.61
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.50
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.90
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.76
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.89
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.57
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.44
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.34
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.31
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.01
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.53
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.48
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.58
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.43
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.59
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.11
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.50
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.42
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.40
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12170.55
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.07
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.03
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000132040
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.88
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000034255
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:47.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195297294.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27727
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    4.18
 p-value of test no 33                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.47
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.03
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.69
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.81
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.73
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.23
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.85
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.89
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.21
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.65
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.82
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.05
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.09
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.95
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.78
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.35
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907836
   j =  2                              :            46076
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399908001
   j =  2                              :            45989
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
 p-value of test no 106                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.62
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.52
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.95
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.11
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.09
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.64
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.85
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.64
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.83
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17834.10
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.15
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.46
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.33
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.56
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.26
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.46
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.23
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.66
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.32
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.80
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.41
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.66
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.75
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.68
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.22
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.75
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.02
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.65
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.32
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.84
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.43
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.28
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.23
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.17
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.64
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.56
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.26
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.41
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9728.21
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.01
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.92
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.04
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.91
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.71
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.70
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.41
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.27
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999895478
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.27
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999987068
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9920
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:25.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196313102.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27728
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4476
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.67
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.38
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.59
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.60
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.11
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.63
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.73
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.78
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.56
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.28
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5195.56
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908311
   j =  2                              :            45843
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907906
   j =  2                              :            46044
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.83
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.88
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.09
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.71
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.51
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.58
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.33
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.30
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.70
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.64
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17773.61
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.71
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.89
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.15
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.14
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.02
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.02
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.20
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.74
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.27
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.18
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.42
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.24
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.17
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.22
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.15
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.92
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.84
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.66
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.42
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.22
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.44
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.75
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.78
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.00
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.69
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.37
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.40
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  299.14
 p-value of test no 174                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.39
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.62
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.30
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.50
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.02
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.13
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.71
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.36
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.92
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.47
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.80
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.92
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.75
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.31
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000016867
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.80
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999956087
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:35.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197263374.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27729
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.87
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.34
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.63
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.23
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.19
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.66
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.64
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.60
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.01
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.76
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.60
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.23
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.63
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.85
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908201
   j =  2                              :            45895
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908062
   j =  2                              :            45963
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 115                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.37
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.92
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.81
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.83
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.01
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.84
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.97
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.47
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.63
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.08
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.69
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17719.27
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.89
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.20
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.08
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.82
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.73
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.95
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.02
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.85
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.92
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.24
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.45
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.46
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.30
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.31
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.51
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.36
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   87.47
 p-value of test no 164                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.61
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.67
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.46
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.53
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.87
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.04
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.94
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.45
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.15
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.62
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.49
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.18
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.08
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.00
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.36
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.17
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.87
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.24
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.05
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.07
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.56
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.57
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.62
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.56
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.74
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000152854
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.53
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999968777
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.32e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:34.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198311950.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27730
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    4.13
 p-value of test no 30                 :  7.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.85
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.66
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.52
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.32
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.30
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.01
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.46
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.09
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.70
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.31
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.20
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.16
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.33
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907952
   j =  2                              :            46015
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908838
   j =  2                              :            45569
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.79
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.67
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.54
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.95
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.48
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.18
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.99
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.59
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.99
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.14
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.41
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.98
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.48
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.76
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.96
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.80
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.01
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.51
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.81
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.79
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.85
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.21
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.12
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.64
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.71
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.88
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.30
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.03
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.95
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.91
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.30
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.24
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.40
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.31
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.35
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.19
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.62
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.48
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.24
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.68
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.77
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.59
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.04
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.010
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.30
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.37
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.75
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.02
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11630.79
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.05
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.42
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999971513
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.49
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999860375
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:48.50
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199360526.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27731
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    3.12
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.53
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.49
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.18
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.11
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.14
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.09
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.14
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.04
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.32
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.77
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.77
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.71
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.00
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908231
   j =  2                              :            45877
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46187
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870187
   j =  1                              :        399907628
   j =  2                              :            46183
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 79                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  8.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 99                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.28
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.80
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.68
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.80
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.59
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.10
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.07
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.08
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17029.87
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.32
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.81
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.21
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.55
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.45
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.65
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.16
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.36
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.33
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.54
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.67
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.49
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.35
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.78
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.86
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.40
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.33
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.42
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5193.43
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.19
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.95
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.43
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.99
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.07
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.46
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.08
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   30.18
 p-value of test no 176                :  2.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.56
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.16
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.06
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9750.73
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.37
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.32
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.27
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.46
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11517.45
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12149.45
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.29
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000048049
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.34
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000070744
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:14.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200474638.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27732
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7558
 p-value of test no 19                 :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.30
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.50
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.10
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.71
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.89
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.42
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.48
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.30
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.60
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.50
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.80
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.33
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908099
   j =  2                              :            45943
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908558
   j =  2                              :            45712
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.67
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.56
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.73
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.89
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.77
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.82
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.34
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 126                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    5.66
 p-value of test no 128                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   16.82
 p-value of test no 129                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.10
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.16
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.79
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.10
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.46
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.97
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.35
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.90
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.90
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.03
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.59
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.96
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.88
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.68
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.00
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.01
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.81
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.34
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.33
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.47
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.50
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.06
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.06
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.88
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.68
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.15
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.55
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.20
 p-value of test no 189                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-4
 p-value of test no 194                :    0.9915
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.27
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.13
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.67
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.41
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.24
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.50
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.89
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.78
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4300.56
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.39
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12100.77
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.21
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000005299
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.57
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999949319
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:50.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  66  MatrixRank, L=30, r=0           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201490446.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27733
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5282
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7081
 p-value of test no 19                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.35
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 30                 :    0.9960
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.72
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.22
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.78
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.70
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.35
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.37
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.77
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.90
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.63
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.34
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.80
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.38
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.53
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.48
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908533
   j =  2                              :            45732
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46395
 p-value of test no 71                 :  8.2e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870395
   j =  1                              :        399907215
   j =  2                              :            46385
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.32
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.68
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.51
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.47
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.42
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.97
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17157.27
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.15
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.69
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.79
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.63
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.26
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.31
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.13
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.92
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.04
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.39
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.58
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.07
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.03
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.22
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.13
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.67
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.73
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.06
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.81
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.03
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.64
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.08
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.45
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.44
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.58
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.11
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.86
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.62
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9923
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.58
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.23
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.48
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.76
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.17
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.26
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.25
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.99
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.98
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.01
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11580.80
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12242.13
 p-value of test no 230                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.22
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999963107
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.62
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000036136
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.053
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:52.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202539022.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27734
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.12
 p-value of test no 26                 :    0.9998    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.30
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.29
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.70
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.36
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.44
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.32
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.63
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.81
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.11
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.81
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.70
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.47
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.67
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4769.21
 p-value of test no 68                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908220
   j =  2                              :            45890
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908285
   j =  2                              :            45850
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.75
 p-value of test no 115                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.075
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.78
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.59
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.32
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.65
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.64
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.55
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 131                :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.44
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.52
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.04
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.96
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.31
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.64
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.55
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.67
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.79
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.62
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.35
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.84
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.95
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.41
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.86
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.12
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.29
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.21
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.51
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.92
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.70
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.70
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.85
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.61
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.17
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.13
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.68
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.79
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.61
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.49
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.30
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.01
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.54
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.22
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 185                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.00
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.78
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.39
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.28
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.50
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.17e-5
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.20
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.35
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.16
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.35
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.57
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.63
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.29
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999923261
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000012772
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:14.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203620366.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27735
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5272
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.65
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9935
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.10
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.71
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.99
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.56
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.01
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.74
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.19
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.52
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.25
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.30
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   21.35
 p-value of test no 66                 :  6.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.74
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.36
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  7.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908273
   j =  2                              :            45859
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45368
 p-value of test no 71                 :    0.9916
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869368
   j =  1                              :        399909267
   j =  2                              :            45362
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.86
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.79
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.68
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.15
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.82
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.51
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.08
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.38
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.44
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.86
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.24
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.82
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.68
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.45
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.88
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.15
 p-value of test no 151                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.45
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.81
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.23
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.12
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.93
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.64
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.35
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.03
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.16
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.56
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.82
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.79
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.00
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.08
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.11
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.27
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.60
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.99
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.50
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.62
 p-value of test no 172                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.17
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.14
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.61
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.87
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 180                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 182                :  5.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.79
 p-value of test no 183                :    0.9974
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.21
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.30
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.20
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.07
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.37
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.33
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.32
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.25
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.96
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.25
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.03
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000127015
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.71
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000092245
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:13.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              6.9e-4
  43  Permutation, t = 10             7.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204668942.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27736
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.17
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.04
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.92
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.27
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.83
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.06
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.78
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.45
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.75
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.24
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.07
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.75
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.84
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.90
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45981
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908040
   j =  2                              :            45977
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908265
   j =  2                              :            45863
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.65
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.18
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.92
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.98
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.32
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.65
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.33
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.17
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.65
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.61
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.47
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.90
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.75
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.18
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.14
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.56
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.71
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.91
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.99
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.89
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.87
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.09
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.81
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.23
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.43
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.63
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.62
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.24
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.38
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.72
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.39
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.33
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.46
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.05
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.51
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.69
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.51
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.72
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.43
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.64
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.47
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.38
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.55
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.29
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.24
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.48
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.12
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.10
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11466.12
 p-value of test no 230                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.33
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999947363
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.92
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999925499
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    2.08
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:54.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205717518.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27737
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5553
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.50
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.09
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.35
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.25
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.45
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.22
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6823.42
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.86
 p-value of test no 58                 :  5.4e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    7.74
 p-value of test no 60                 :  1.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :    9.05
 p-value of test no 61                 : 1 -  7.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.34
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.34
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5188.28
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908362
   j =  2                              :            45816
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908134
   j =  2                              :            45924
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.11
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.38
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.80
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.52
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.59
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.54
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.90
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.09
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.86
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.79
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17612.49
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.65
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.84
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.71
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.85
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.80
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.09
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.53
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.50
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.63
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.57
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.86
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.31
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.56
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.57
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.43
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.34
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.15
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.96
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.89
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.45
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.75
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.60
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.14
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.38
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.62
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.76
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.55
 p-value of test no 178                :    0.9980
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.34
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.21
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.89
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.92
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.80
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.44
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.89
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.69
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.95
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.73
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.60
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999970628
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.92
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000047563
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 241                :    0.9910
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.48
 p-value of test no 243                :    0.9935
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.073
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:54.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  38  Run, r = 0                     1 -  7.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206766094.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27738
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.79
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.29
 p-value of test no 51                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.95
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.51
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.71
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.55
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.31
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.92
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.39
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.21
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.82
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.99
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.93
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908850
   j =  2                              :            45572
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908103
   j =  2                              :            45941
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.62e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.13
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.30
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.10
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.40
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.56
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.54
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.66
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 126                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.26
 p-value of test no 129                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.61
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.72
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17126.38
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.25
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.57
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.42
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.99
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.18
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.59
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.26
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.11
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.30
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.88
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.21
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.37
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.57
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.93
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.84
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.22
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.96
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.66
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.25
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.46
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.38
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.18
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.28
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.98
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.16
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.63
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.76
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.43
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.09
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.86
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.28
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.09
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.10
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.90
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.85
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.32
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.87
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.24
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.66
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.96
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.42
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999922772
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.33
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000000967
 
 Normal statistic for number of bits   : 7.64e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 245                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:44.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207814670.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27739
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.86
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.86
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.36
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.49
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.54
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.98
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.61
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.00
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.78
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.50
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.26
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.65
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.33
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.41
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45471
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869471
   j =  1                              :        399909061
   j =  2                              :            45465
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907845
   j =  2                              :            46073
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-4
 p-value of test no 109                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    4.51
 p-value of test no 111                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.35
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.43
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.69
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.57
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.42
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.23
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.53
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.65
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.07
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.91
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.25
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.96
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.93
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.09
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.10
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.84
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.93
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.11
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.02
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.91
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.33
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.01
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.77
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.18
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.96
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.03
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.81
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.94
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.58
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.51
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.72
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.99
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.08
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.51
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.83
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.58
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.57
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.37
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.59
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.53
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.41
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.04
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.61
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 212                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10276.70
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.37
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.62
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.27
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.91
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.60
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.65
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.80
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000053551
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.83
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999937076
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:13.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208830478.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27740
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9945
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.09
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.97
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.08
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.22
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.54
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.13
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1535.23
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6905.69
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.72
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.11
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.76
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.04
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.10
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907911
   j =  2                              :            46043
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908299
   j =  2                              :            45849
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.86
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.49
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.29
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.46
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.73
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.99
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.75
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.63
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.93
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.07
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.77
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.51
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.62
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.19
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.82
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.67
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.59
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.67
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.11
 p-value of test no 156                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.06
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.02
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.66
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.54
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.24
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.28
 p-value of test no 162                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.12
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.64
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.87
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.49
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.16
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.64
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.77
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.58
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.75
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.17
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.41
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.62
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.63
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.06
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.36
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 200                :  8.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    4.68
 p-value of test no 202                :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.93
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.88
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.10
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.12
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.38e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.01
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.10
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.53
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.34
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.47
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.42
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.60
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000164611
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.95
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999995264
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 250                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:23:24.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189366287.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27741
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 7                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.27
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.60
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.64
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.45
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   89.34
 p-value of test no 52                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.98
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.05
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.16
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.17
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.72
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.91
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.50
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.19
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.93
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4678.69
 p-value of test no 68                 :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907729
   j =  2                              :            46128
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907962
   j =  2                              :            46016
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.68
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.74
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.14
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.63
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.81
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.08
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.48
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17236.40
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.26
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.82
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.02
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.71
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.99
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.17
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.46
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.83
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.28
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.36
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.19
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.83
 p-value of test no 162                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.11
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.88
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.79
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.10
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.70
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.61
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.33
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.69
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.60
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.09
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4773.13
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.94
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.89
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.13
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.57
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.40
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.46
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.38
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.34
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.74
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.21
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.89
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.08
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.01
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.15
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.95
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999875852
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.26
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000013852
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 236                :  9.8e-4    *****
 
 Anderson-Darling statistic = A2       :    4.56
 p-value of test no 237                :  4.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.45
 p-value of test no 238                :  7.2e-3
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:53.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190873615.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27742
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5527
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    3.27
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.87
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   24.06
 p-value of test no 46                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.67
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.92
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.23
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.32
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.13
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.69
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.22
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.79
 p-value of test no 58                 :  4.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    5.43
 p-value of test no 60                 :  2.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   11.81
 p-value of test no 61                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.29
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.42
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.15
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908524
   j =  2                              :            45735
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907883
   j =  2                              :            46054
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
 p-value of test no 76                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.43
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.87
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.03
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.08
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.65
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.72
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.31
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.10
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.04
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.74
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.63
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.63
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.38
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.79
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.04
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.81
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.88
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.98
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.17
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.81
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.03
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.14
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.55
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.11
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.91
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.58
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.07
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.68
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.53
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.26
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.66
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.86
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.70
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.39
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.87
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.37
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.96
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.72
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.58
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.27
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.65
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.85
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 201                :    0.9952
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.55
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.06
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10255.69
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.73
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.76
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.02
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.64
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.84
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.34
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.12
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.36
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000032581
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.12
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999952898
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:59.86
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191922191.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27743
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9945
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.57
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.52
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.91
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.12
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.54
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.19
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7101.40
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.33
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.49
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.51
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.35
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908658
   j =  2                              :            45662
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908438
   j =  2                              :            45775
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.09
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.66
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.59
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.00
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.96
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.14
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.09
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.84
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.15
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.51
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.18
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.82
 p-value of test no 149                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.00
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.10
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.20
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.06
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.03
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.30
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.26
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.64
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.65
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.14
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.01
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.72
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.57
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.68
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.03
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.10
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.38
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.32
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.73
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.63
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.99
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.39
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.04
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.45
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.61
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.08
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.04
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 192                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.96
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.95
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.84
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 205                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  151.33
 p-value of test no 207                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.84
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.95
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.33
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.81
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.07
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3966.49
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.37
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.49
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.55
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999927383
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.21
 p-value of test no 233                :  4.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999935795
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.074
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.22
 p-value of test no 239                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:11.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  84  Fourier3, r = 0                 0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193003535.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27744
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.44
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.56
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.06
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.86
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.62
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.13
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.65
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  502.96
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.68
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.15
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 58                 :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.03
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.76
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.45
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.36
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4919.68
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908095
   j =  2                              :            45948
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908158
   j =  2                              :            45915
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
 p-value of test no 80                 :    0.9959
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9943
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-4
 p-value of test no 100                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.79
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.20
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.84
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.25
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.59
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.72
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.07
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.03
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.43
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.81
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.30
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.93
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.16
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.25
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.76
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.22
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.05
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.26
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.88
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.85
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.34
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.86
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.27
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.06
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.03
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.89
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.97
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.23
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.36
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.19
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.03
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.81
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.81
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.99
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.06
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.39
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.54
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.83
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.65
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.14
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 204                :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.20
 p-value of test no 207                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.03
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.55
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.10
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.01
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.65
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.13
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.44
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12080.84
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.31
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999922604
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.82
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000050158
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    2.11
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:20.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194019343.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27745
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.06
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.74
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.16
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.17
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.34
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.60
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.22
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.16
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.61
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.91
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.22
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.92
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.54
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4863.17
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907988
   j =  2                              :            46000
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907732
   j =  2                              :            46128
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 95                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9975
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.14
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.82
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.32
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.91
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.10
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.35
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.85
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.46
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17369.54
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.75
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.80
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.34
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.51
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.51
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.15
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.52
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.79
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.87
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.58
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.71
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.85
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.11
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.26
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.12
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.24
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.14
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.94
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.14
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.11
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.78
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.02
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.39
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.99
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.07
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.90
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.66
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.33
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.86
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.87
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.13
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.83
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.19
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.86
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.36
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.14
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.60
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.42
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.77
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.53
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.21
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.02
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.95
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999938849
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.70
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999981671
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    2.39
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194904079.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27746
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.60
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.50
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.09
 p-value of test no 48                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.49
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.45
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.12
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.67
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.82
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.06
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.50
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.86
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.93
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.60
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.50
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45568
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869568
   j =  1                              :        399908866
   j =  2                              :            45564
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907837
   j =  2                              :            46068
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.32
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.59
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.94
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.37
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.13
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.73
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.24
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.67
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.93
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.73
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17431.74
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.60
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.99
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.29
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.34
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.93
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.12
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.36
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.67
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.02
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.53
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.92
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.28
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.07
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.10
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.22
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.63
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.29
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.41
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.59
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.76
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.24
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.45
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.21
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.20
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.93
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.95
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.46
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.14
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.88
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.09
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.27
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.11
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.78
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.47
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.12
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.00
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.63
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.70
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.80
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000007681
 
 Normal statistic for number of bits   :   0.061
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.17
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000157690
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:06.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195887119.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27747
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7141
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.94
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    3.89
 p-value of test no 26                 :  9.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.09
 p-value of test no 41                 :  8.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.20
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.11
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.93
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.44
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.43
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1336.21
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.87
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.29
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.34
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.95
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.52
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.67
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45463
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869463
   j =  1                              :        399909076
   j =  2                              :            45459
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908319
   j =  2                              :            45833
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 86                 :  8.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    5.33
 p-value of test no 88                 :  2.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9975
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-6
 p-value of test no 110                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 111                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.30
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.58
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.62
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.61
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.37
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.34
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.59
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.27
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.53
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17651.59
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.50
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.64
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.80
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.31
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.78
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.76
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.37
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.82
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.19
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.36
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.99
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.16
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.72
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.78
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.32
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.49
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.41
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.55
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.80
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.38
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.19
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.48
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.65
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.43
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.11
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.03
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.32
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.80
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.28
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.33
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.30
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.25
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.78
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.68
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.35
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.44
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.32
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.31
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12088.72
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.17
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000092860
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.26
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999966152
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:35.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196837391.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27748
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.23
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.86
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.43
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  187.33
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.47
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.87
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.44
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   50.62
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.33
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.51
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.72
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5142.06
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908591
   j =  2                              :            45700
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46234
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870234
   j =  1                              :        399907536
   j =  2                              :            46226
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.23
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.60
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.01
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.09
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.47
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.26
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.59
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.44
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.24
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.23
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.88
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.06
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.37
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.05
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.72
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.16
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.21
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.28
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.12
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.22
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.62
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.36
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.22
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.28
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.64
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.41
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.95
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.03
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.37
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.01
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.35
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.27
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.31
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.61
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.46
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.51
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.30
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.82
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.07
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.81
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.20
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.52
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.46
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.33
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.00
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.70
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.29
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000011155
 
 Normal statistic for number of bits   :   0.088
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.96
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000064363
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.79
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:26.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197820431.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27749
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5617
 p-value of test no 13                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.69
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.80
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.13
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.57
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.79
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.48
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.22
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.19
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.96
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.05
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.23
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.87
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.25
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.13
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46205
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870205
   j =  1                              :        399907594
   j =  2                              :            46197
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908592
   j =  2                              :            45695
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.73
 p-value of test no 117                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.91
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.69
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.09
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.84
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.07
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.52
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.31
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.21
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.91
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17262.23
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.39
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.44
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.97
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.09
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.07
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.62
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.63
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.12
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.52
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.70
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.61
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.68
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.48
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  193.19
 p-value of test no 159                :  9.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.12
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.16
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.95
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.81
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.84
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.53
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.61
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.65
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.11
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.13
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.22
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  470.72
 p-value of test no 171                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.50
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.94
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.71
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.28
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.80
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.84
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.89
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.68
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.74
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.87
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.00
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.40
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.86
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.49
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.74
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.27
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.64
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000056125
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.85
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999764966
 
 Normal statistic for number of bits   :   -1.86
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    2.14
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 240                :  3.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    6.19
 p-value of test no 242                :  8.6e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.28
 p-value of test no 243                :    0.9995    *****
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:03.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     9.2e-4
  104  AutoCor, d=3, r=0               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198901775.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27750
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.73
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.20
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.29
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.45
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.48
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.99
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.46
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.85
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.72
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.71
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.10
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.11
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.65
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.88
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.10
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908439
   j =  2                              :            45779
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908415
   j =  2                              :            45785
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.67
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.27
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.94
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.66
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.25
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.91
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.28
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.47
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17379.46
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.36
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.43
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.68
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.80
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.12
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.74
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.65
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.76
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.90
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.36
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.44
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.13
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.14
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.49
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.14
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.18
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.20
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.47
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.04
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.85
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.54
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.84
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.83
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.70
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.91
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.61
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4812.55
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.97
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.77
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.67
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 181                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.75
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.67
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.08
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.87
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.78
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.70
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.80
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.85
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.87
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.29
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.80
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.83
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000028849
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.87
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000025747
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.056
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 251                :    0.9926
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.64
 p-value of test no 253                :    0.9958
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200343567.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27751
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4159
 p-value of test no 14                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.97
 p-value of test no 23                 :  3.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.70
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.27
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.04
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.37
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.32
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.17
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.41
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.20
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7114.96
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.07
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.18
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.31
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.21
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.03
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907858
   j =  2                              :            46062
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908222
   j =  2                              :            45880
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-4
 p-value of test no 90                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.62
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.39
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.41
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.41
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.48
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.69
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.11
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.73
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.15
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 134                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.19
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17052.91
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.37
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.43
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.68
 p-value of test no 148                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.01
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.45
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.45
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.63
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.51
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.13
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.26
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.30
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.12
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.15
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.37
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.51
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.24
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.35
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.12
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.45
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.68
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.15
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.45
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.78
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.50
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.32
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.78
 p-value of test no 172                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5203.53
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  303.51
 p-value of test no 174                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.01
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.42
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.88
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.77
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.95
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.86
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.48
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.75
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.36
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.69
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.05
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.02
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.56
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000045475
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.60
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999996644
 
 Normal statistic for number of bits   :  -0.027
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:16.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201392143.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27752
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.62
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.86
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.37
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.92
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.79
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.10
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.75
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.18
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.49
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.63
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.15
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.83
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399907999
   j =  2                              :            45999
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9946
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-6
 p-value of test no 113                :    0.9969
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.18
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.44
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.27
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.37
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.35
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.03
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.78
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.13
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.64
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.48
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.59
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.17
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.41
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.73
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.42
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.58
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.67
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.57
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.06
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.14
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.75
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.18
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.44
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.38
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.09
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.28
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.03
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.97
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.68
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.57
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.30
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.18
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.62
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.01
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.53
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.94
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.39
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.15
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.52
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.46
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.15
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.95
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.68
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.91
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.02
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999928703
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.03
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999987227
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:37.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202473487.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27753
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 6                  :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.93
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.43
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.03
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.16
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.80
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.21
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.98
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.88
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.80
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.96
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.44
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.53
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.65
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.65
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.95
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46217
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870217
   j =  1                              :        399907571
   j =  2                              :            46207
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907911
   j =  2                              :            46037
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.42e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.63
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.78
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.61
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.78
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.57
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.55
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.78
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.87
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.92
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.78
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.64
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.47
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.22
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.23
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.23
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.85
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.25
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.21
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.58
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.81
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.20
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.57
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.99
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.23
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.25
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.35
 p-value of test no 164                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.32
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.67
 p-value of test no 166                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.91
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.67
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.82
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.86
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.34
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.93
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.64
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.02
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.80
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.30
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.77
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.84
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.45
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.30
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10208.31
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.53
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.34
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.92
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.79
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.98
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11397.93
 p-value of test no 229                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.25
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.27
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000165973
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.91
 p-value of test no 233                :  3.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999987905
 
 Normal statistic for number of bits   :  -0.096
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203456527.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27754
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 39                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.04
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.07
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.89
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.09
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.16
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.92
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.13
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.35
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.03
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.15
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.13
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.30
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.19
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.29
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908753
   j =  2                              :            45622
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908689
   j =  2                              :            45648
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 91                 :    0.9931
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-5
 p-value of test no 110                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.87
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.48
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.82
 p-value of test no 121                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.42
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.05
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.91
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.79
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.54
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.02
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.87
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.94
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.28
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.79
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.85
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.60
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.32
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.18
 p-value of test no 156                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.69
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.28
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.73
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.80
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.82
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.62
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.34
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.72
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.40
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.58
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.17
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.96
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.15
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.60
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.43
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.13
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.90
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.92
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.38
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.02
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    2.24
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.28
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.95
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.60
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.98
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.48
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.12
 p-value of test no 218                :  9.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.92
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.77
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.63
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.08
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.10
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.24
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.42
 p-value of test no 231                :  9.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000037582
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.72
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999930242
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    2.58
 p-value of test no 249                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9987
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:54.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  94  HammingCorr, L = 1200           9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204472335.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27755
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 4                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1240
 p-value of test no 12                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334360
   j =  1                              :        599997520
   j =  2                              :             1240
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    5.95
 p-value of test no 24                 :  1.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     975
 p-value of test no 25                 :  7.0e-3
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.99
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.87
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.40
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.80
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.28
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.16
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.66
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.64
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.88
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.97
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.84
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.72
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.99
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.77
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46160
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907681
   j =  2                              :            46158
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908556
   j =  2                              :            45716
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 77                 :    0.9912
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 78                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9901
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-5
 p-value of test no 112                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.96
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.66
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.19
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.17
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.32
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.35
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.10
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.94
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.88
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.23
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.01
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17232.51
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.98
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.28
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.32
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.74
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.19
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.80
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.34
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.15
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.20
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.26
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.71
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.31
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.71
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.92
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.75
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.35
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.42
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.55
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.77
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.12
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.39
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.07
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.30
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.38
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.15
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.33
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.87
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.45
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.66
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.43
 p-value of test no 179                :  7.6e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 185                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 188                :  6.2e-3
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.55
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.71
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.06
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.88
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.27
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.80
 p-value of test no 217                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.52
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.60
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.49
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.53
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.49
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.18
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.69
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000107509
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.55
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999942527
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:02.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205455375.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27756
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.36
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.24
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.89
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.91
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.71
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.94
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.66
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.04
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.49
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.49
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.56
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 62                 :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    5.48
 p-value of test no 64                 :  1.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   30.91
 p-value of test no 65                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.24
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.66
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.99
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907902
   j =  2                              :            46046
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
 p-value of test no 94                 :    0.9969
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.99
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.85
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.01
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.39
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.33
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.51
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.58
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.69
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.63
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.94
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17672.63
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.12
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.38
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.03
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.67
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.11
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.61
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.61
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.57
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.88
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.06
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.31
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.96
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.69
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.99
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.06
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.34
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.86
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.72
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.13
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.78
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.73
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.38
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.36
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.96
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.18
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.33
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.61
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.47
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.87
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.82
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.43
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.35
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.49
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.22
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.69
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.65
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.20
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.92
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.01
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.32
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.31
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000002224
 
 Normal statistic for number of bits   :   0.018
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.12
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999950030
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    2.23
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9949
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:50.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206536719.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27757
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 23                 :    0.9967
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    3.41
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.05
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.73
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.12
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.60
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.34
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.46
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.25
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.61
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.36
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.18
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.76
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  159.75
 p-value of test no 67                 :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4917.10
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46279
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870279
   j =  1                              :        399907447
   j =  2                              :            46269
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907733
   j =  2                              :            46129
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 93                 :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9916
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.95
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.95
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.28
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.76
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.52
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.44
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.52
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.87
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.21
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17532.11
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.28
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.22
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.36
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.39
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.72
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.78
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.30
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.77
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.33
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.98
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.69
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.43
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.38
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.04
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.84
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.91
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.69
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.76
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.86
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.88
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.86
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.21
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.56
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.77
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.22
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.59
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.95
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.89
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.14
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.17
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.52
 p-value of test no 178                :    0.9906
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 192                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.59
 p-value of test no 198                :  3.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.07
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.92
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.51
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.00
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 220                :  3.7e-3
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 221                :  4.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5152.74
 p-value of test no 222                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.27
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.48
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.08
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.43
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.53
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.68
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999936908
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.04
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000066580
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:12.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  84  Fourier3, r = 0                 0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207552527.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27758
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.9913
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     259
 p-value of test no 37                 :    0.9914
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.07
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.73
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.35
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.10
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.95
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.99
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.62
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.05
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.98
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 63                 :  7.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 64                 :  2.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.58
 p-value of test no 65                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.24
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.19
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908882
   j =  2                              :            45556
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908168
   j =  2                              :            45910
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 101                :    0.9964
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.52
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.52
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.72
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.70
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.38
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.88
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.41
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.60
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.91
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.23
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.54
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.32
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.85
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.78
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.63
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.22
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.27
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.88
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.96
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.97
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.95
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.44
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.56
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.69
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.33
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.17
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.67
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.08
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.43
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.61
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.95
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.15
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.79
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.82
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.58
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.33
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.31
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.93
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.74
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10180.84
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.96
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.10
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.88
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.32
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.47
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.27
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.80
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000123289
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.67
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000085849
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:34.43
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208535567.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27759
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.08
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.61
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.82
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :  104.23
 p-value of test no 51                 :  4.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.99
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.58
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.50
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.60
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.89
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.92
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.76
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.60
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.33
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.84
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46366
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870366
   j =  1                              :        399907273
   j =  2                              :            46356
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45479
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869479
   j =  1                              :        399909045
   j =  2                              :            45473
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
 p-value of test no 104                :    0.9958
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.63
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.76
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.13
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.77
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.20
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.62
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.94
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.20
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.37
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.61
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17212.05
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.79
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.15
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.72
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.40
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.05
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.61
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.48
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.92
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.54
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.60
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.90
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.32
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.26
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.49
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.88
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.30
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.88
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.27
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.31
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.16
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.36
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.40
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.30
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.35
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.63
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.69
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.07
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.26
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.26
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.96
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.86
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.43
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.95
 p-value of test no 222                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.52
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4344.33
 p-value of test no 227                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.24
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.62
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.94
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.08
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000143065
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.92
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000037681
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:58:30.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         4.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209584143.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27760
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5586
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.99
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.77
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.23
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.62
 p-value of test no 49                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.63
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.08
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.21
 p-value of test no 52                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.84
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.26
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1577.40
 p-value of test no 56                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.95
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.85
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.67
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.08
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.83
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908629
   j =  2                              :            45678
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45526
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908950
   j =  2                              :            45522
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.25
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.78
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.28
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.51
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.44
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.50
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.94
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.80
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.39
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.97
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.72
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.81
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.24
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.87
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.25
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.89
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.88
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.47
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.98
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.28
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.46
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.19
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.42
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.20
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.58
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.70
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.63
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.69
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.08
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.60
 p-value of test no 169                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.10
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.23
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.17
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.45
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.50
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.19
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.99
 p-value of test no 178                :  7.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.65
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.22
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.71
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.87
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.72
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.56
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.54
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.74
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.13
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.32
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.13
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.63
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999994418
 
 Normal statistic for number of bits   :  -0.044
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.35
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000072013
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:56.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189399056.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27761
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.12
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.48
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.47
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.61
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.23
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.30
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.08
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.25
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.96
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.05
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.10
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.67
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.62
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46319
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870319
   j =  1                              :        399907369
   j =  2                              :            46305
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907975
   j =  2                              :            46008
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.49
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.73
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.34
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.97
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.46
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.82
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.04
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.70
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.73
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.92
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.68
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.33
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.85
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.24
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.92
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.63
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.48
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.36
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.70
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.52
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.42
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.87
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.11
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.55
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.75
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.73
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.97
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.10
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.04
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.98
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.65
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.49
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.57
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4813.93
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.61
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.14
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.38
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.20
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.33
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.18
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.17
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.92
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.75
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.16
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.64
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.65
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.98
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11484.85
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12147.90
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.89
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000040327
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.62
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999944330
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 241                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 243                :  8.4e-3
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:26.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190087184.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27762
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    3.82
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.60
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.63
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.59
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.38
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.92
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.12
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.81
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.15
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.21
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.41
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.24
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.68
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.56
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.31
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46267
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870267
   j =  1                              :        399907468
   j =  2                              :            46263
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908374
   j =  2                              :            45810
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.58
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.12
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.84
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.01
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.66
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.14
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.69
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.52
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17379.37
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.18
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.43
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.14
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.29
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.58
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.13
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.81
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.24
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.31
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.84
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.64
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.13
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.40
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.89
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.12
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.03
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.16
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.51
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.31
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.73
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.18
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.63
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.32
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.69
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.99
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.18
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.02
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.78
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.66
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.68
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-3
 p-value of test no 219                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5108.92
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.22
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.33
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.90
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.10
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.07
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.67
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999877424
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.19
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999973958
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.068
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    2.25
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:02.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191037456.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27763
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 11                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.05
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.32
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.86
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.49
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.58
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.14
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.86
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.11
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.09
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6830.79
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.59
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.91
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.45
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.30
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.15
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46070
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870070
   j =  1                              :        399907864
   j =  2                              :            46062
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908456
   j =  2                              :            45766
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.53
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.76
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.96
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.80
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.64
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.20
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.55
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.73
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 142                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17975.95
 p-value of test no 145                :  1.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.28
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.73
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.48
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.74
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.16
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.62
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.92
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.34
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.95
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.30
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.38
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.56
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.95
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.97
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.43
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.78
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.57
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.24
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.98
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.37
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.87
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.81
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.72
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.90
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.67
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.05
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.06
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.40
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.10
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.23
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.98
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.10
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.84
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.78
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.40
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10198.88
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.10
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.63
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3919.27
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.30
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.29
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.81
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.77
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000104989
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.91
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999989591
 
 Normal statistic for number of bits   :  -0.082
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:38.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192118800.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27764
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.52
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.71
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.61
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.44
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.40
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.87
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.92
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.80
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.34
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7402.26
 p-value of test no 57                 :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.88
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.57
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.38
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.42
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908398
   j =  2                              :            45798
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45698
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869698
   j =  1                              :        399908609
   j =  2                              :            45688
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.33
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.12
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.12
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.02
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.39
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.67
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.40
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.65
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.71
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.68
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.15
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.06
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.85
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.71
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.99
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.51
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.52
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.02
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.56
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.90
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.64
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.65
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.18
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.74
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.94
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.12
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.36
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  304.33
 p-value of test no 166                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.64
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.53
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.97
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.80
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.01
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.68
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.45
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.19
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.12
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.47
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.16
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.42
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.15
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.96
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9821.08
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.99
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.03
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.02
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.42
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.87
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.32
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.68
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999929594
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.42
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999993089
 
 Normal statistic for number of bits   :  -0.055
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 245                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 246                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 247                :  1.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.14
 p-value of test no 248                :  8.4e-4    *****
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:39.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  105  AutoCor, d=1, r=27              8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193429520.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27765
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 12                 :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.66
 p-value of test no 46                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.60
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.56
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.66
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.99
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.85
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.73
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.28
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.09
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.32
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.99
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.13
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.64
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5312.11
 p-value of test no 68                 :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908216
   j =  2                              :            45889
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908133
   j =  2                              :            45932
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.89
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.49
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.14
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.71
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.61
 p-value of test no 123                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.50
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.93
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.54
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.97
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.66
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 142                :  6.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17065.22
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.85
 p-value of test no 146                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.74
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.93
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.40
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.25
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.08
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.54
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.78
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.68
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.97
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.95
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.88
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.87
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.04
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.71
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.85
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.66
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.39
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.28
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.52
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.83
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.60
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.36
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.07
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.62
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.45
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.50
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.11
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 186                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    5.23
 p-value of test no 187                :  2.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.76
 p-value of test no 188                :  2.9e-3
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.56
 p-value of test no 196                :    0.9916
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.80
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.32
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.43
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.60
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.60
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.97
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.09
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.78
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.81
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.29
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11599.81
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.56
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000074356
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.72
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999989480
 
 Normal statistic for number of bits   :  -0.083
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:03.71
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194347024.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27766
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     343
 p-value of test no 37                 :  8.0e-3
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.57
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.68
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.34
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.96
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.60
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.27
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.99
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.75
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.80
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.80
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.06
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.68
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.83
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908262
   j =  2                              :            45866
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907802
   j =  2                              :            46096
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.07
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.91
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.00
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.55
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.28
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.79
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.67
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.05
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.94
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.44
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17500.61
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.03
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.53
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.06
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.80
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.26
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.98
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.80
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.81
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.04
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.00
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.51
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.49
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.38
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.21
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.48
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.95
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.35
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.95
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.15
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.17
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.55
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.80
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.09
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.00
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.91
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.21
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.52
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.25
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.17
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.85
 p-value of test no 179                :    0.9978
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.59
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.93
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.81
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.31
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.27
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.21
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.64
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.77
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.83
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.14
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.59
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.90
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.65
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999843014
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000050692
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:57.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195362832.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27767
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    5.22
 p-value of test no 32                 :  2.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.31
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.12
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.68
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.43
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.70
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.75
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.43
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.82
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6863.49
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.75
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.31
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.18
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5090.06
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907699
   j =  2                              :            46146
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46221
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870221
   j =  1                              :        399907559
   j =  2                              :            46219
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-6
 p-value of test no 112                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.49
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.40
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.75
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.65
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.49
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.35
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 126                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    6.90
 p-value of test no 128                :  4.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   16.98
 p-value of test no 129                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.08
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.78
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.09
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.83
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.71
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.24
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.45
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.60
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.47
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.57
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.96
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.64
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.26
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.64
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.34
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.01
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.90
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.14
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.15
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.78
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.71
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.86
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.19
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.66
 p-value of test no 165                :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.15
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.72
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5259.75
 p-value of test no 168                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.60
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.70
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.02
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.54
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.26
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.08
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.32
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.80
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.19
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.84
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.04
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.83
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.35
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.53
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.43
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.37
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.10
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.12
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.98
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.14
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999968864
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.67
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999952004
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:14.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  66  MatrixRank, L=30, r=0           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196378640.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27768
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.76
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9912
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.44
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.33
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.18
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.71
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.75
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.55
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.79
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.19
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.01
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.30
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.41
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.74
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908162
   j =  2                              :            45910
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908556
   j =  2                              :            45722
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.62
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.98
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.63
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.10
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.70
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.41
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.34
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.44
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.87
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.53
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.26
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.62
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.27
 p-value of test no 149                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.72
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.31
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.35
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.75
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.69
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.06
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.43
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.72
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.59
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.06
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.92
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.51
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.37
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.58
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.89
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.50
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.26
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.49
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.95
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.58
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.74
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.43
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.38
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.61
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.33
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.79
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.12
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.34
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.95
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.10
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.27
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.14
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 223                :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5128.03
 p-value of test no 226                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3969.55
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.96
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.44
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.37
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.38
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999829985
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.75
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999943799
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:50.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197591056.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27769
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 8                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.29
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.16
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   25.80
 p-value of test no 50                 :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.48
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.41
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.90
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.06
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6724.98
 p-value of test no 57                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.16
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.89
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.01
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.59
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.58
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46160
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907686
   j =  2                              :            46148
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908333
   j =  2                              :            45817
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.43
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.73
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.32
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.74
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.00
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.57
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.97
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.37
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.14
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.43
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17643.30
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.81
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.44
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.07
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.03
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.61
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.66
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.29
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.51
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.89
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.57
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.44
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.45
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.82
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.59
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.04
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.22
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.55
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.82
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.05
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.95
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.17
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.41
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.87
 p-value of test no 170                :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.55
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.09
 p-value of test no 172                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.18
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.69
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.52
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.78
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.01
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.82
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.90
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.15
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.97
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.75
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.25
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.03
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.01
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.05
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.79
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.09
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.99
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999981551
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.88
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000169063
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.035
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:22.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198541328.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27770
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 7                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4200
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    3.09
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 38                 :    0.9948
 
 Stat. AD after spacings (mNP2-S)      :    4.94
 p-value of test no 39                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.48
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.60
 p-value of test no 49                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.83
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.33
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.98
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.32
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.55
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6875.90
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.75
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.48
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.60
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.99
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908460
   j =  2                              :            45767
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907728
   j =  2                              :            46130
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.06
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.46
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.53
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.25
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.40
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.34
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.51
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.98
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.79
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17249.28
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.24
 p-value of test no 147                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.16
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.26
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.51
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.17
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.04
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.39
 p-value of test no 154                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.53
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.93
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.96
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.87
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.13
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.85
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.32
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.00
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.30
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.57
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.84
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.32
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.39
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.22
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.68
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.54
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.42
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.10
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.06
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.54
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.18
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.08
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.45
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.67
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.49
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.27
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.34
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.68
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.89
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.68
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.73
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.61
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.93
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.43
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000289909
 
 Normal statistic for number of bits   :    2.29
 p-value of test no 232                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.67
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000152827
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199524368.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27771
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    3.43
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.19
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.46
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.27
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.60
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.43
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1336.98
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.15
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.82
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.19
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.88
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.11
 p-value of test no 67                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.87
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45568
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869568
   j =  1                              :        399908865
   j =  2                              :            45566
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908232
   j =  2                              :            45878
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :  8.8e-3
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.12
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.54
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.49
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.54
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.29
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.92
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.12
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.56
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.48
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17282.67
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.40
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.35
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.80
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.98
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.71
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.94
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.19
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.50
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.35
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.20
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.18
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.74
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.68
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.83
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.74
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.22
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.33
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.17
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.34
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.92
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.13
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.04
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.63
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.54
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.55
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.40
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.47
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.43
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.47
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.37
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.77
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.74
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.08
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.86
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.86
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.20
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.64
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.01
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.05
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.88
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.98
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999954404
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.85
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999921014
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.094
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:59.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200507408.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27772
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    3.32
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.28
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.35
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.42
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.06
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.45
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.22
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.57
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.12
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6868.22
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.61
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.45
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.14
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.02
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.75
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908679
   j =  2                              :            45656
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908782
   j =  2                              :            45597
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.81
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.62
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.41
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.51
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.86
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.67
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.66
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.64
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.21
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.12
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.39
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.66
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.04
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.48
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.30
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.15
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.58
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.59
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.03
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.36
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.21
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.51
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.96
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.90
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.36
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.94
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.53
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.26
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.44
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.11
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.59
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.48
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.94
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.04
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.74
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.97
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.13
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.95
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.05
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.94
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.70
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.81
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.46
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.06
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.41
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.75
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.20
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 223                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 225                :  8.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5174.86
 p-value of test no 226                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.74
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.52
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.80
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.52
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.13
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000145582
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.46
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999959852
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:50.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201621520.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27773
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 6                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7622
 p-value of test no 21                 :  2.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.77
 p-value of test no 46                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.74
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.46
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.18
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.43
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.28
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.51
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.15
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.69
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.18
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.97
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.50
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.06
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908043
   j =  2                              :            45977
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908648
   j =  2                              :            45673
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 73                 :    0.9912
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.00
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.10
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.84
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.40
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.07
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.49
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.93
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.43
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.54
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.23
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17023.04
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.48
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.16
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.40
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.86
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.79
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.75
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.99
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.07
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.07
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.10
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.69
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.41
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.89
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.48
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.31
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.52
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.30
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.89
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.05
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.14
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.30
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5257.28
 p-value of test no 168                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.84
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.53
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.73
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.05
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.46
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.07
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.54
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.93
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.58
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-4
 p-value of test no 181                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.78
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.74
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.37
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.32
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.47
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.24
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5097.01
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.76
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.95
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.56
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11448.10
 p-value of test no 230                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.91
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999924473
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.64
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000150436
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:01.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202670096.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27774
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.39
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.21
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.13
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.11
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.48
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.75
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.31
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.03
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.72
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.78
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.77
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.64
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.76
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5204.61
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908387
   j =  2                              :            45796
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908620
   j =  2                              :            45681
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
 p-value of test no 86                 :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.67
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.00
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.63
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.69
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.64
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.17
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.14
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.97
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.68
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17805.24
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.43
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.36
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.68
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.36
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.31
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.78
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.46
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.54
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.50
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.29
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.51
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.94
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.39
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.47
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.49
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.96
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.47
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.15
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.77
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.31
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.42
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.77
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.26
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.60
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.75
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.20
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.23
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.63
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.65
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.67
 p-value of test no 179                :  3.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.35
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.14
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.66
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.59
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.90
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.35
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.58
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.81
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.84
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.73
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.86
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000015286
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.11
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999985532
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:24.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203685904.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27775
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.71
 p-value of test no 29                 :  1.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.00
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.22
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.53
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.05
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.60
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.20
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.00
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7235.85
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.69
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.38
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.57
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.79
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.67
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907847
   j =  2                              :            46069
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908451
   j =  2                              :            45767
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.85
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.77
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.11
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.62
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.82
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.22
 p-value of test no 125                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.90
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.06
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.33
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17612.06
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.89
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.89
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.34
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.56
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.16
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.32
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.56
 p-value of test no 153                :  3.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.92
 p-value of test no 156                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.59
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.47
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.00
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.07
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.59
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.63
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.53
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.28
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.50
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.18
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.03
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.64
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.56
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.45
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.67
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.28
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.27
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.55
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.81
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.61
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.02
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.43
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.19
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.91
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10225.38
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9773.17
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.57
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.07
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3917.23
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.87
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.10
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.35
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.57
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000162106
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.64
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999987143
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:35.30
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204996624.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27776
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.24
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.08
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.00
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.06
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.90
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.87
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.05
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.02
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7114.18
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.20
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.80
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.74
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.56
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5182.40
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907868
   j =  2                              :            46057
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908195
   j =  2                              :            45901
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 72                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.02e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.10
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.44
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.26
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.10
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.23
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.70
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.82
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.91
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17084.33
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.86
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.42
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.00
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.32
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.68
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.64
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.37
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.48
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.17
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.28
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.95
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.16
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.30
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.01
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.19
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.60
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.83
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.75
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.24
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.98
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.35
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.14
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.30
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.78
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.82
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.45
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.80
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.33
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.21
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.85
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.40
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.04
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.05
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.01
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.12
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.01
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.37
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.15
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.76
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.42
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11682.45
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.30
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.72
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000200623
 
 Normal statistic for number of bits   :    1.59
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.51
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000050032
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.79
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:59.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206143504.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27777
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.25
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.26
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.61
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.37
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.91
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.72
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7330.76
 p-value of test no 57                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.82
 p-value of test no 58                 :  1.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    6.39
 p-value of test no 60                 :  7.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   10.41
 p-value of test no 61                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.63
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.36
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.78
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.32
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46285
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870285
   j =  1                              :        399907434
   j =  2                              :            46277
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908509
   j =  2                              :            45738
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.78
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.77
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.57
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.76
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.48
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.60
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.58
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.13
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17178.96
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.19
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.35
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.49
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.14
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.64
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.75
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.37
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.08
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.49
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.16
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.65
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.06
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.93
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.43
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.36
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.10
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.68
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.98
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.52
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.94
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.99
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.27
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.33
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.74
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.43
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.67
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.38
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.14
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.87
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.38
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.06
 p-value of test no 179                :    0.9989
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.45
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.87
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.37
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.79
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.23
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.63
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.48
 p-value of test no 217                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.19
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.95
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4306.87
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.04
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.87
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.16
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.01
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000010129
 
 Normal statistic for number of bits   :   0.080
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.50
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000097399
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:30.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  38  Run, r = 0                      0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207159312.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27778
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    5.42
 p-value of test no 26                 :  1.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.46
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.96
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.54
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.39
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.72
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.87
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.98
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.22
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.65
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.55
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.93
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7263.56
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.12
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.73
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.33
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.23
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.60
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908185
   j =  2                              :            45900
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908363
   j =  2                              :            45811
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 95                 :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.39
 p-value of test no 119                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.44
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.30
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.76
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.24
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.22
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.73
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.60
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   95.26
 p-value of test no 141                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17380.73
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.30
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.71
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.45
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.96
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.14
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.90
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.87
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.13
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.42
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.89
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.49
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.58
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.93
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.79
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.61
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.10
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.12
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.95
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.77
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.85
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.38
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.76
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.41
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.26
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.21
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.95
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.12
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.22
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.35
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.58
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.83
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.19
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.25
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.67
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.56
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.01
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.02
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.78
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.69
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.34
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.71
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.37
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000012694
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.96
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000003376
 
 Normal statistic for number of bits   :   0.027
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 237                :    0.9973
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:49.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208175120.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27779
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 19                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.93
 p-value of test no 23                 :  9.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   27.20
 p-value of test no 46                 :  3.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.23
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.34
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.79
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.03
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.17
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6879.85
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.53
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.37
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.54
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.79
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908398
   j =  2                              :            45798
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907738
   j =  2                              :            46122
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.85
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.21
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.93
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.25
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.32
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.84
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.05
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.36
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.92
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.51
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17152.08
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.76
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.56
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.50
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.04
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.84
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.38
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.25
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.74
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.11
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.96
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.98
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.93
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.51
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.44
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.89
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.61
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.11
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.36
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.86
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.35
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.93
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.63
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.25
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.51
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  267.23
 p-value of test no 175                :  1.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.78
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.66
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.89
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.61
 p-value of test no 198                :    0.9907
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.88
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.06
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10310.62
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.40
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    5.96
 p-value of test no 221                :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4569.60
 p-value of test no 222                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.40
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.05
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.17
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11601.73
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.12
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.14
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999931970
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.75
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999998672
 
 Normal statistic for number of bits   :  -0.010
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:21.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                3.1e-4
  95  HammingIndep, L=30, r=0         0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209223696.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27780
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    3.88
 p-value of test no 38                 :  9.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.02
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.96
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.27
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.39
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.27
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.81
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.54
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.69
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.51
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
 p-value of test no 62                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.01
 p-value of test no 65                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.78
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.33
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5238.82
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45536
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869536
   j =  1                              :        399908930
   j =  2                              :            45532
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908272
   j =  2                              :            45864
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.82
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.77
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.13
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.26
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-3
 p-value of test no 126                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.96
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.90
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17559.87
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.69
 p-value of test no 146                :    0.9955
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.49
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.80
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.14
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.58
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.93
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.09
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.52
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.81
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.69
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.20
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.03
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.60
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.64
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.16
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.10
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.87
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.88
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.84
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.26
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.02
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.57
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.28
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.63
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.44
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.75
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.15
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.10
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.87
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.49
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.10
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.03
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.75
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.43e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.92
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.23
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.75
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.42
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.35
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.82
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.67
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000031912
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.11
 p-value of test no 233                :  8.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999764519
 
 Normal statistic for number of bits   :   -1.86
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:48.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189431825.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27781
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5562
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4480
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.53
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.52
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.66
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.36
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.35
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.16
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.64
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.29
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.51
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.41
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.43
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.27
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.28
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 63                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.15
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.83
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.07
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908098
   j =  2                              :            45945
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45367
 p-value of test no 71                 :    0.9917
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869367
   j =  1                              :        399909270
   j =  2                              :            45359
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.08
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.95
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.53
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.59
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.87
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.43
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.75
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.32
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.72
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17528.15
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.48
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.89
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.07
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.90
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.21
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.02
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.93
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.37
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.61
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.84
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.80
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.97
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.18
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.99
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.03
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.58
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.45
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.33
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.50
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.62
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.88
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.35
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.52
 p-value of test no 169                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.12
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.16
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.00
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.39
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.79
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.65
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 183                :    0.04
 
 Sample variance                       :    2.09
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.90
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.34
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 204                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 206                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.74
 p-value of test no 207                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.66
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.02
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.79
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.26
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.16
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.03
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.97
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.39
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.14
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000037795
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.69
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999926648
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:31.92
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190513169.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27782
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    3.58
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     528
 p-value of test no 31                 :    0.9985
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    3.12
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.74
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.03
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.61
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.67
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.91
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.43
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.02
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.69
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.59
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.91
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.34
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.26
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.04
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.96
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45329
 p-value of test no 70                 :    0.9949
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869329
   j =  1                              :        399909348
   j =  2                              :            45317
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908751
   j =  2                              :            45617
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 106                :  9.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 108                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.56
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.04
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.14
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.32
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.99
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.92
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.91
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.11
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.53
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.62
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.34
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.99
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.55
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.71
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   54.87
 p-value of test no 154                :  3.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.04
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.36
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.62
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.23
 p-value of test no 159                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.73
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.45
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.13
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.47
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.75
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.85
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.19
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.57
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.67
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.87
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.93
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.28
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.45
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.63
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.90
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.41
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.70
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.56
 p-value of test no 177                :  5.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.67
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.18
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.46
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.23
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.11
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.91
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.47
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.31
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.42
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.80
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11489.82
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.43
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.29
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999960992
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.42
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000120403
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:18.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191823889.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27783
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.41
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     819
 p-value of test no 25                 :    0.9967
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.49
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.87
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.10
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.36
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.92
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.19
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.68
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.58
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.64
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.30
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.23
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.49
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907940
   j =  2                              :            46024
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.23
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.99
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.59
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.76
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.90
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.50
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.92
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.14
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.13
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.09
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.13
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.73
 p-value of test no 150                :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.04
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.36
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.44
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.25
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.57
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.07
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.00
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.41
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.28
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.89
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.83
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.06
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.80
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.05
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.92
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.84
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.72
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.58
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.53
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.82
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.24
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.56
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.07
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.44
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 187                :  6.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.85
 p-value of test no 188                :    0.9978
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.11
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.08
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.82
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.33
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.41
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.39
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.57
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.17
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.21
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.95
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12147.63
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.96
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.39
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000031972
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.06
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000007279
 
 Normal statistic for number of bits   :   0.058
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:28.93
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192774161.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27784
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 12                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 14                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.80
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.41
 p-value of test no 35                 :  5.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    4.34
 p-value of test no 38                 :  6.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.62
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.23
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.25
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.35
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.80
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.48
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1342.77
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6885.99
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.04
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.04
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.63
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  167.97
 p-value of test no 67                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.01
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908561
   j =  2                              :            45715
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908007
   j =  2                              :            45989
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.67
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.15
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.55
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.09
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.72
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.64
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.92
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.98
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.56
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.13
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.71
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.48
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.86
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.76
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.42
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.03
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.04
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.86
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.58
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.82
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.19
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.34
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.70
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.00
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.09
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.61
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.50
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.78
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.16
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  303.83
 p-value of test no 169                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.63
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.48
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.81
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.75
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.80
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.93
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.72
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.40
 p-value of test no 177                :  8.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.08
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.15
 p-value of test no 184                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.23
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.89
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.76
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.33
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.90
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5100.62
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.61
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.82
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.48
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.74
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.69
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.57
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999981233
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.35
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000254113
 
 Normal statistic for number of bits   :    2.01
 p-value of test no 234                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:26.61
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193822737.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27785
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 12                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4147
 p-value of test no 14                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.56
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.40
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.46
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.95
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.80
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.01
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.09
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.90
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.18
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.07
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.65
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.02
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.11
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4887.55
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45509
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869509
   j =  1                              :        399908985
   j =  2                              :            45503
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45533
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869533
   j =  1                              :        399908937
   j =  2                              :            45527
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.89
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.81
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.40
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.10
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.06
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.11
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.77
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.89
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.66
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.28
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17766.13
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.05
 p-value of test no 146                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.92
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.98
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.55
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.06
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.20
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.81
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.30
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.31
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.01
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.43
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.14
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.62
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.45
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.22
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.07
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.97
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.80
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.62
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.46
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.05
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.22
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.50
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.74
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.23
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.33
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.45
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.73
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.80
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.16
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.77
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.35
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.01
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.61
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.68
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.65
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.87
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.21
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.95
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999963581
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.53
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999912077
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.73
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195067921.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27786
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.50
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.28
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.30
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.66
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.90
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.92
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.64
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.92
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.51
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.95
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.65
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.21
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.51
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.06
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.51
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45464
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869464
   j =  1                              :        399909074
   j =  2                              :            45460
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907961
   j =  2                              :            46012
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.98e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.20
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.01
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.73
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.17
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.27
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.04
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.69
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.93
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.09
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.69
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.87
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.25
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.90
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.88
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.66
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.71
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.94
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.91
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.19
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.56
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.14
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.05
 p-value of test no 159                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.50
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.96
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.54
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.21
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.31
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.14
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.04
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.64
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.51
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.80
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.10
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.52
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.25
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.98
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.66
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.89
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.66
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.53
 p-value of test no 198                :  8.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.95
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.77
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.22
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.96
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.02
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.90
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.18
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.72
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.96
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.66
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.38
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999899690
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.11
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000049624
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:14.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196050961.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27787
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    3.52
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.40
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.97
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.77
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.01
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.35
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.22
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.76
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.76
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.33
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.72
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.77
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.94
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.99
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908293
   j =  2                              :            45852
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908404
   j =  2                              :            45795
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.94
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.30
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.14
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.76
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.70
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.03
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.85
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.09
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.42
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.23
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17420.44
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.57
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.81
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.88
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.02
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.03
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.53
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.35
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.56
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.48
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.83
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.98
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.73
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.81
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.84
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.73
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.72
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.77
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.08
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.03
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.18
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.27
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.79
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.40
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.29
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.47
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.77
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.41
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.66
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.62
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.14
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.31
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.79
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.20
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.70
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.66
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.86
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.91
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.55
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4337.53
 p-value of test no 227                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.83
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.22
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.92
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.81
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000054361
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.79
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999957677
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    2.23
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:49.15
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196968465.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27788
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1235
 p-value of test no 12                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334355
   j =  1                              :        599997530
   j =  2                              :             1235
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.22
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.46
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.70
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.49
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.63
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.83
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.62
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.09
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.55
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.51
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.03
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.38
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.57
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.49
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.42
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907781
   j =  2                              :            46102
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46306
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870306
   j =  1                              :        399907391
   j =  2                              :            46300
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.24
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.63
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.59
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.52
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.34
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.74
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.81
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.65
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.29
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.86
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.04
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.90
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.70
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.35
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.74
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.36
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.10
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.02
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.13
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.79
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.05
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.13
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.35
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.76
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.88
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.64
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.75
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.68
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.95
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.04
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.43
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.66
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.90
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.00
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.18
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.03
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.40
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.49
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.52
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.48
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.06
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.83
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.98
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.67
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.25
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.58
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.83
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.81
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5092.75
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.53
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3928.63
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.46
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.23
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.58
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.65
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000025126
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.97
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000021094
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:54.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198279185.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27789
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    4.23
 p-value of test no 33                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.20
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.05
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.48
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.85
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.06
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.65
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.81
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.50
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.54
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.22
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.97
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.68
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907760
   j =  2                              :            46111
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908500
   j =  2                              :            45741
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.71
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.61
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.27
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.23
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.69
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   64.78
 p-value of test no 125                :  1.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.82
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.99
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.40
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.35
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.34
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.57
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.61
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.73
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.72
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.11
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.35
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.71
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.25
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.07
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.94
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.71
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.58
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.83
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.19
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.32
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.22
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.18
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.39
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.75
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.12
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.17
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.17
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.53
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.02
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.77
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.87
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.70
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.65
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.53
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.75
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.22
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.72
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.87
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.37
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.22
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.32
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.43
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11483.71
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.58
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.43
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000049522
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.80
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000139360
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:08.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    1.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199262225.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27790
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4213
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.35
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.03
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.13
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.73
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.39
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.70
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.80
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.49
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.31
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.63
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.26
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.70
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.56
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.91
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46070
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870070
   j =  1                              :        399907864
   j =  2                              :            46062
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908598
   j =  2                              :            45692
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 86                 :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
 p-value of test no 87                 :    0.9954
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 88                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9973
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.13
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.02
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.68
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.70
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.25
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.18
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.21
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.00
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.81
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.15
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17554.35
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.42
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.20
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.22
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.29
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.94
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.41
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.65
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.40
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.78
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.82
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.46
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.78
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.81
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.27
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.12
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.00
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.45
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.38
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.40
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.18
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.82
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.44
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.08
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.50
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.48
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.30
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.39
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.08
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.65
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.33
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.17
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.26
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.73
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 225                :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5187.16
 p-value of test no 226                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.49
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.50
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.71
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.59
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.00
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000080599
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999936830
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:03.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200212497.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27791
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    3.54
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.71
 p-value of test no 47                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.27
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.74
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.50
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.16
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.58
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.78
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.48
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.18
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.71
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.12
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.97
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.22
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.86
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.03
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907749
   j =  2                              :            46121
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908544
   j =  2                              :            45725
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  4.6e-3
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 88                 :  8.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  9.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.43
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.72
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.13
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.33
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.79
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.86
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.96
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.61
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.30
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.86
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.37
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.18
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.04
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.35
 p-value of test no 151                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.12
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.92
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.18
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.22
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.09
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.79
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.13
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.03
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.79
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.99
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.01
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.12
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.06
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.38
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.60
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.04
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.87
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.72
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.80
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.37
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.78
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.73
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.77
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.44
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.05
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.43
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.74
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9740.20
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.18
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.80
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.80
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.61
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.80
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11424.03
 p-value of test no 229                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.96
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.79
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000012184
 
 Normal statistic for number of bits   :   0.096
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.60
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999895664
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:13:43.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201261073.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27792
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     356
 p-value of test no 37                 :  9.0e-4    *****
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    4.23
 p-value of test no 45                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.66
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.08
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.32
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.60
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.58
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.62
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.55
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.96
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.54
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.01
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.53
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.53
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.31
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908433
   j =  2                              :            45782
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46246
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870246
   j =  1                              :        399907513
   j =  2                              :            46236
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.21
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.56
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.21
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.11
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.54
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.36
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.57
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.44
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.08
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.25
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.67
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.78
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.59
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.55
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.57
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.23
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.64
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.25
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.30
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.32
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.55
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.35
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.94
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.40
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.07
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.51
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.84
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.61
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.62
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.26
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.13
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.61
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.24
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.47
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.32
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.76
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.35
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.40
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.091
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.39
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.87
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.21
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.30
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10198.98
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.42
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.75
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.56
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.96
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.09
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.77
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.76
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999933398
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.70
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999968630
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-4
 p-value of test no 235                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.33
 p-value of test no 238                :  9.9e-3
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:42.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NJumps, t = 9        9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202407953.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27793
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.33
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.09
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.49
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.40
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.92
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.41
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.52
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.98
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.63
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.71
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.28
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.88
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46284
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870284
   j =  1                              :        399907434
   j =  2                              :            46280
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.16
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.26
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.20
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.20
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.42
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.11
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.59
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.53
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.98
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.74
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.58
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.16
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.58
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.37
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.62
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.46
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.29
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.70
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.91
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.52
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.33
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.68
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.65
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.64
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.82
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.27
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.34
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.23
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.67
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.64
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.03
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.15
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.10
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.07
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.30
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.17
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.90
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.89
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.28
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.56
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.15
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.33
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.31
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.14
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.17
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.83
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.97
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.85
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.93
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.16
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12042.39
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.46
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.44
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000030988
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.23
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000117874
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 250                :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:40.90
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203390993.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27794
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.65
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.13
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.39
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.68
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.86
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.91
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.53
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.18
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.54
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.47
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.90
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.75
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.83
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.85
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.90
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5195.26
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908667
   j =  2                              :            45659
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45186
 p-value of test no 71                 :    0.9994    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869186
   j =  1                              :        399909634
   j =  2                              :            45174
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9908
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.62
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.63
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.83
 p-value of test no 122                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.62
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.49
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.61
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.07
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.42
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.33
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17342.84
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.59
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.39
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.61
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.51
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.14
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.91
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.54
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.00
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.65
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.49
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.49
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.99
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.13
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.63
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.91
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.29
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.30
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.31
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.78
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.32
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.65
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.10
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.25
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.72
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.78
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.59
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.88
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 204                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.30
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.20
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.78
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.56
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.04
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.20
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.52
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.06
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.43
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.90
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999844235
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.43
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999978941
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:55.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  45  CollisionPermut, r = 10         0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204439569.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27795
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.05
 p-value of test no 22                 :  8.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.26
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.08
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.69
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.67
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.50
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.09
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.35
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.72
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.14
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6875.01
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.69
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.57
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.62
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.07
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908298
   j =  2                              :            45845
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45526
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908949
   j =  2                              :            45524
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.32
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.75
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.74
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.15
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.13
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.65
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.27
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.19
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    4.82
 p-value of test no 144                :  3.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.37
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.33
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.00
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.29
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.45
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.04
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.62
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.26
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.43
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.78
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.67
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.59
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.35
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.51
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.21
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.69
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.25
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.33
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.34
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.46
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.81
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.90
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.16
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.93
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.13
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.65
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.40
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.46
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.33
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.05
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.31
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.14
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.09
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.86
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.83
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.79
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.01
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.28
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.13
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4702.81
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.70
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.15
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.41
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.53
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999967736
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.62
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999901004
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.089
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:41.44
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205389841.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27796
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4151
 p-value of test no 14                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.71
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.49
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.24
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.18
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.48
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.26
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.28
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.16
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.10
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.62
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.93
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.93
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.51
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.45
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908430
   j =  2                              :            45779
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45569
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908868
   j =  2                              :            45557
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 86                 :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.81e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.66
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.10
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.13
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.19
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.69
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.97
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.75
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.54
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.77
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.36
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.97
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17731.53
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.02
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.52
 p-value of test no 147                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.36
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.96
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.51
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.84
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.47
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.23
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.84
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.57
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.87
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.69
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.35
 p-value of test no 162                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.60
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.88
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.25
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.61
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.67
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.57
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.45
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.13
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.61
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.84
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.20
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.29
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.58
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.87
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.06
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.83
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.57
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.18
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.01
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.46
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.07
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 224                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.15
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4241.49
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.24
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.99
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.75
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.64
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999959849
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.14
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000004282
 
 Normal statistic for number of bits   :   0.034
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.077
 p-value of test no 248                :    0.47
 
 Sample variance                       :    2.11
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:35.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206372881.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27797
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.16
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.86
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.23
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.03
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.54
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.71
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.02
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.56
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6791.23
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.90
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.73
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.22
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.30
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.66
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908361
   j =  2                              :            45818
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908322
   j =  2                              :            45836
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.73
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.20
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.22
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.03
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.67
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.46
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.50
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.08
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.83
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.93
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.28
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.32
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.40
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.59
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.30
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.18
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.31
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.08
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.24
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.60
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.26
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.08
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.43
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.55
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.10
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.80
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.53
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.28
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.21
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.72
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.93
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.62
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.60
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.78
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.63
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.02
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.92
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.18
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.71
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.28
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.88
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
 p-value of test no 212                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10293.12
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.91
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.42
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.05
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.60
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.93
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.21
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.14
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999862286
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.45
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999956504
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:12.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207519761.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27798
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7100
 p-value of test no 21                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    7.48
 p-value of test no 36                 :  2.1e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     255
 p-value of test no 37                 :    0.9957
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.36
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.47
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.72
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.34
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.40
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.65
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.86
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.99
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.07
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.21
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908222
   j =  2                              :            45883
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908343
   j =  2                              :            45818
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 100                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.42
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.32
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.47
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.00
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.97
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.45
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.87
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.54
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.06
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-4
 p-value of test no 142                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 143                :  1.7e-4    *****
 
 Anderson-Darling statistic = A2       :    7.39
 p-value of test no 144                :  2.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18113.63
 p-value of test no 145                :  1.5e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.81
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.03
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.94
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.45
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.06
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.05
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.43
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.64
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.78
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.92
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.68
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.33
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.80
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.74
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.96
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.39
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.01
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.82
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.59
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.85
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.76
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.22
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.02
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.64
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.28
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.04
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.21
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.67
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.39
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.75
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.61
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.40
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.34
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.07
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.95
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.43
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11549.78
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.14
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.31
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000098413
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.33
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000054841
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 8.48e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:11.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          2.1e-4
  73  GCD                             1.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208732177.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27799
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1492
 p-value of test no 10                 :  3.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334612
   j =  1                              :        599997016
   j =  2                              :             1492
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 44                 :    0.9962
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.94
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.26
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.64
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.77
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.53
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.09
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.51
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.65
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.12
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.70
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.52
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4809.73
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908502
   j =  2                              :            45740
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908025
   j =  2                              :            45986
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 83                 :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.13
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.13
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.83
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.97
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.32
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.13
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.59
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.39
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.25
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17647.22
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.48
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.93
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.34
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.97
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.73
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.20
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.69
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.13
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.08
 p-value of test no 157                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.27
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.85
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.13
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.93
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.12
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.12
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.49
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.44
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.74
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.09
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.10
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.89
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.27
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.74
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.30
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.54
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  142.53
 p-value of test no 175                :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.62
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.29
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.44
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9931
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.68
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.03
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.15
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10269.46
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.39
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.10
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.64
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.26
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.15
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.72
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.53
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.44
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000052249
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.00
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999945344
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:58:12.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           3.4e-4
  79  RandomWalk1 C (L=10000, r=15)   0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209715217.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27800
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 10                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7102
 p-value of test no 15                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.83
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.01
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.07
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.12
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.72
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.70
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.89
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.34
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.46
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.25
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.35
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.19
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.10
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.93
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.44
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.19
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908681
   j =  2                              :            45652
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908246
   j =  2                              :            45868
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.74
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.49
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.74
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.14
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.66
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.13
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.038
 p-value of test no 134                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.99
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.83
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.92
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.04
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.03
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.93
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.36
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.20
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.83
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.76
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.19
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.61
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.76
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.68
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.60
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.32
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.59
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.68
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.95
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.43
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.36
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.70
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.86
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.27
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.04
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.42
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.74
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.96
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.23
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.24
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.96
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.57
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.07
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.64
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.81
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.44
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.80
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.15
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.27
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.55
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.00
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.57
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.77
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.83
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.79
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.12
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000079216
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.07
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999836978
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:33.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189464594.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27801
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7542
 p-value of test no 18                 :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.86
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.79
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.22
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.47
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.64
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.29
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.78
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1554.09
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.52
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.65
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.83
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.92
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.20
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4808.16
 p-value of test no 68                 :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908626
   j =  2                              :            45678
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908368
   j =  2                              :            45810
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-6
 p-value of test no 113                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.075
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.58
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.39
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.11
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.65
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.97
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.63
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.02
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.04
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.48
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.72
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17230.21
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.26
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.77
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.92
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.42
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.91
 p-value of test no 153                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.18
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.97
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.41
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.54
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.92
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.82
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.76
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.37
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.09
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.70
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.27
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.49
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.44
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.49
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.81
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.17
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.03
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.86
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.62
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    2.57
 p-value of test no 184                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.95
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.92
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.38
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.42
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10334.15
 p-value of test no 215                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.34
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.83
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.01
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.72
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.78
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12060.03
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.92
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999974780
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.68
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000000547
 
 Normal statistic for number of bits   : 4.32e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 236                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    6.75
 p-value of test no 237                :  4.7e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.42
 p-value of test no 238                :  3.1e-4    *****
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:08.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0               3.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190185490.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27802
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5532
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.21
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.61
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.54
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.92
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.27
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.74
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.08
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6873.59
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.81
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.32
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.52
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.73
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45549
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869549
   j =  1                              :        399908904
   j =  2                              :            45545
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.10
 p-value of test no 116                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.32
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.43
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.37
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.07
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.65
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.49
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.74
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.92
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.41
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.52
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.16
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.29
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.18
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.07
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.91
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.77
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.68
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.61
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.96
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.79
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.50
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.46
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.33
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.77
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.49
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.90
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.42
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.27
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.91
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.92
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.36
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.52
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.44
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.68
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.14
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.63
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.52
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.81
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 180                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.84
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 202                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.33
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.05
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.20
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10229.06
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.89
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.17
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.34
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.22
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.81
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.04
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.89
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000021427
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.91
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000009415
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 241                :    0.9934
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:30.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191463442.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27803
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 18                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.10
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.96
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.41
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.55
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.78
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.99
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.97
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.74
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.36
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.77
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.85
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.71
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.42
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.87
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908182
   j =  2                              :            45906
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907779
   j =  2                              :            46106
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-6
 p-value of test no 112                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.93
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.64
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.87
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.40
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.53
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.20
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.05
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.68
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.01
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17080.46
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.31
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.41
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.10
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.46
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.22
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.44
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.52
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.63
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.39
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.30
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.90
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.78
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.96
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.85
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.39
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.43
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.77
 p-value of test no 164                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.93
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.94
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.66
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.20
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.22
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.03
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.44
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.13
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.25
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.60
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.19
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.73
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.97
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.11
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.66
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.38
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.90
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.78
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.84
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.64
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.73
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.26
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.56
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.52
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999870386
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.51
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999923024
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.88
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:02.11
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192151570.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27804
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4488
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.99
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.67
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.71
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.02
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.91
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.20
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.86
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.77
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.58
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6920.03
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.89
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.38
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.81
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.53
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907670
   j =  2                              :            46159
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908771
   j =  2                              :            45610
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.45
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.03
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.46
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.89
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.63
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.12
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.65
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.64
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.27
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17674.36
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.02
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.74
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.68
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.50
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.94
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.13
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.70
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.71
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.69
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.12
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.69
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.78
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.29
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.92
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.19
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.77
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.79
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.18
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.60
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.16
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.87
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.51
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.40
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.04
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.39
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.05
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.48
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.81
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.97
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.70
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.67
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.26
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.02
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.21
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.50
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.41
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.22
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.18
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   92.19
 p-value of test no 231                :  9.3e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999944219
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.48
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999961790
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:02.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  101  Run of bits, r = 0              9.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193232914.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27805
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.14
 p-value of test no 23                 :    0.9991    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    3.30
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :    1000
 p-value of test no 25                 :  5.5e-4    *****
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.47
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.75
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.45
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.32
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.69
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.68
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.44
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.12
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.36
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.84
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.19
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4926.48
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908712
   j =  2                              :            45635
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908258
   j =  2                              :            45868
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 103                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.31
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.35
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.05
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.85
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.73
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.75
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.06
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.12
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.93
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.24
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.00
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.74
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.10
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.23
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.72
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.41
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.38
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.93
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.89
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.47
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.61
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.86
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.36
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.56
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.06
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.49
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.78
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.38
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.80
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.59
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.18
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.23
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.45
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.01
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.53
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.60
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.98
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.86
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.54
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.53
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.88
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.15
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.40
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.50
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.32
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.47
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.89
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.54
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.20
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.78
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000003934
 
 Normal statistic for number of bits   :   0.031
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.76
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999901391
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 235                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-3
 p-value of test no 240                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.56
 p-value of test no 243                :  5.2e-3
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.60e-4
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:28.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           0.9991 
  22  ClosePairs NJumps, t = 3        5.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194379794.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27806
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.07
 p-value of test no 29                 :  2.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.33
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.32
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.52
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.82
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.55
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.80
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.03
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.17
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.07
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.23
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.14
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6654.46
 p-value of test no 57                 :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.87
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.11
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.31
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.66
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46185
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907634
   j =  2                              :            46177
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907877
   j =  2                              :            46054
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-6
 p-value of test no 109                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.90
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.76
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.37
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.94
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.27
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.74
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.75
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.95
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.15
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.42
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17642.85
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.74
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.31
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.91
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.07
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.61
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.20
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.80
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.13
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.24
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.79
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.52
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.46
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.47
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.76
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.88
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.38
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.79
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.70
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.33
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.68
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.70
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.96
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.07
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.57
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.76
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.20
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.71
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.31
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.06
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.68
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.06
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
 p-value of test no 219                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    5.28
 p-value of test no 221                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5209.55
 p-value of test no 222                :  7.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.05
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.87
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.51
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.28
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11415.29
 p-value of test no 230                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.29
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000108163
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.85
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999937406
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:22.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  37  Gap, r = 20                     0.9996 
  95  HammingIndep, L=30, r=0         7.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195330066.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27807
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 3                  :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    2.85
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.95
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.97
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.23
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.98
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.63
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.81
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.89
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.05
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.80
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7323.25
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.71
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.22
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.38
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.07
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907934
   j =  2                              :            46030
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908503
   j =  2                              :            45747
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 76                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 99                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.79
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.93
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.70
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.23
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.84
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.10
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.74
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.18
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.75
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.22
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.59
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.77
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.12
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.67
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.52
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.23
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.68
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.39
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.10
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.53
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.28
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.80
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.60
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.04
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.27
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.52
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.15
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.66
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.04
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.11
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.00
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.06
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.60
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.79
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.88
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.47
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.96
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.02
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.85
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.00
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.69
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.78
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.13
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.57
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.83
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.03
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.75
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.85
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.75
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.53
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999910070
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.17
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999971870
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:35.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196509714.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27808
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.05
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.16
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.80
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.98
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.16
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.76
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.84
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.65
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.85
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.03
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.41
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.66
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.68
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908196
   j =  2                              :            45902
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908354
   j =  2                              :            45820
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  9.0e-3
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 78                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.27
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.81
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.14
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.06
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.94
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.93
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.75
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.22
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.58
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.46
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.66
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.61
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.29
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.15
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.89
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.86
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.27
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.29
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.15
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.05
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.46
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.69
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.61
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.31
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.92
 p-value of test no 162                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.70
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.99
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.90
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.56
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.68
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5196.00
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.90
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.67
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.06
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.62
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.77
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.36
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.40
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.04
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.26
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.26
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.69
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.31
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.09
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.80
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.01
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.60
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.98
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.29
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.08
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.73
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.26
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999955991
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999987026
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:52.21
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197525522.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27809
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 40                 :    0.9963
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.35
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.32
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.73
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.09
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.82
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.36
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.76
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.86
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.71
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.74
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.56
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.48
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.07
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.33
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908528
   j =  2                              :            45730
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908315
   j =  2                              :            45838
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 79                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.44
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.07
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.85
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.26
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.63
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.17
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.01
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.35
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17534.22
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.46
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.61
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.52
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.37
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.39
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.60
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.71
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.64
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.03
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.99
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.34
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.04
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.17
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.78
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.00
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.34
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.21
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.15
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.83
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.17
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.36
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.57
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.10
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.03
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5179.05
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.61
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.03
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.44
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.86
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.51
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.39
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.31
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.95
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.31
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.08
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.95
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.36
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3860.91
 p-value of test no 227                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.66
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11394.71
 p-value of test no 229                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.50
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.48
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000039838
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.08
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000001834
 
 Normal statistic for number of bits   :   0.014
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:07.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198574098.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27810
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4146
 p-value of test no 14                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     837
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.75
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.55
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.22
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.62
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.26
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.47
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.83
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.01
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.91
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.06
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.16
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.68
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   75.08
 p-value of test no 67                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.41
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908656
   j =  2                              :            45663
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907969
   j =  2                              :            46011
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.51
 p-value of test no 115                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.81
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.58
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.85
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.27
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.26
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.25
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.65
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.11
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.43
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.78
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.95
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.56
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.24
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.83
 p-value of test no 148                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.90
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.17
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.38
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.67
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.33
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.71
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.65
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.75
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.32
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.31
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.97
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.04
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.98
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.92
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.33
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.63
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.22
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.16
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.39
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.10
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.01
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.43
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.58
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
 p-value of test no 181                :    0.9978
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.13
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.26
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.20
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.38
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.63
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.77
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.92
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.25
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3940.77
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.32
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.67
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.15
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000053362
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.70
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999888476
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:19.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199589906.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27811
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 5                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4162
 p-value of test no 14                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     549
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.14
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.66
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.68
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.81
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.40
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.78
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.70
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.97
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.71
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.16
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.53
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.70
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.91
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908448
   j =  2                              :            45776
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908286
   j =  2                              :            45854
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.75
 p-value of test no 115                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.15
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.16
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.28
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.98
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.73
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.76
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.67
 p-value of test no 134                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.53
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.91
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.75
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.62
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.64
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.52
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.04
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.32
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.53
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.81
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.02
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.35
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.81
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.14
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.08
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.79
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.23
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.65
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.63
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.65
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.27
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.37
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.66
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.95
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.74
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.66
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.51
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.83
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.48
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.13
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.89
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.28
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.18
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.48
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.26
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10193.87
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.16
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.95
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.77
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.29
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.53
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.10
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.75
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.83
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999879374
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.77
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999803066
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:07.89
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200572946.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27812
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.73
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.49
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.34
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.23
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.22
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.43
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.62
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.01
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.71
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.74
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.68
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.54
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.84
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.55
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45450
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909103
   j =  2                              :            45444
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908545
   j =  2                              :            45723
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.42
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.02
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.31
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.47
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.65
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.90
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.82
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.25
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.87
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.71
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.03
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.39
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.98
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.64
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.12
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.94
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.97
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.96
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.22
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.99
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.92
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.42
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.92
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.55
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.68
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.97
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.18
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.27
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.11
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.97
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.07
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.51
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.17
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.25
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.65
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.99
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.80
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.90
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.64
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.15
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.68
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.76
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.93
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.05
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.46
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.02
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.73
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.17
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12285.49
 p-value of test no 229                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.25
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.88
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000061651
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.88
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999976502
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:01.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202145810.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27813
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5609
 p-value of test no 13                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    2.72
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.49
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.16
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.16
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.71
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.85
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.36
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.50
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.20
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.27
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.95
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.04
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.57
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.14
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907888
   j =  2                              :            46053
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908249
   j =  2                              :            45868
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.80e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.80
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.98
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.76
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.97
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.05
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.88
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.22
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.45
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17642.81
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.76
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.30
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.39
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.90
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.86
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.41
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.63
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.19
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.15
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.75
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.85
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.87
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.68
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.95
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.09
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.43
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.67
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.13
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.01
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.21
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.15
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.20
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.71
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.98
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.11
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.08
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.55
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.34
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.80
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.53
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.62
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.09
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.49
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.19
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.61
 p-value of test no 217                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.67
 p-value of test no 218                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.40
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.29
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.52
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.34
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.63
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.94
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.32
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000084199
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.77
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000125362
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:41.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203128850.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27814
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 6                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9902
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.09
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.73
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.80
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.26
 p-value of test no 52                 :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.92
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.19
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.09
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.02
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6771.36
 p-value of test no 57                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.75
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.89
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.60
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5153.65
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908652
   j =  2                              :            45674
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907784
   j =  2                              :            46105
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 108                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.66
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.16
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.61
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.69
 p-value of test no 122                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.60
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.36
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.68
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.94
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17475.60
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.17
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.52
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.81
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.51
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.44
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.14
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.51
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.35
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.08
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.14
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.25
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.13
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.27
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.46
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.47
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.56
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.44
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.12
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.05
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.20
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.97
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.55
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.55
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.47
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.54
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.49
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.49
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.71
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.08
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.51
 p-value of test no 178                :  9.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.83
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.05
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.56
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.85
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.75
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.53
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.52
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 221                :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.17
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.95
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.45
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.63
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.93
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.52
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.55
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999864695
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.73
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000112936
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-3
 p-value of test no 245                :    0.9990
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.38
 p-value of test no 248                :  8.6e-3
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:21.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204079122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27815
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5549
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.10
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.95
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.35
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.87
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.79
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.95
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.13
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.13
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.17
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.23
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.90
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.23
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.61
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.68
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.04
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908027
   j =  2                              :            45982
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45528
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869528
   j =  1                              :        399908947
   j =  2                              :            45522
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
 p-value of test no 91                 :    0.9969
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 92                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
 p-value of test no 98                 :    0.9976
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.95
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.42
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.75
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.46
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.38
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.83
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.60
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.33
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.32
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.75
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.77
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.01
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.24
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.09
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.20
 p-value of test no 149                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.71
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.53
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.81
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.91
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.63
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.40
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.89
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.43
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.02
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.10
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.73
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.54
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.36
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.98
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.79
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.17
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.83
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.20
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.24
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.78
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.27
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.07
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.87
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.27
 p-value of test no 196                :    0.9959
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.04
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.75
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.98
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.19
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.58
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.07
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.61
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.58
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.85
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.46
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.29
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000103288
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.73
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000025672
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:20.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205127698.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27816
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.32
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.65
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.17
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.41
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.24
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.22
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.49
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.00
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.49
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.48
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.99
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.89
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5222.94
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907573
   j =  2                              :            46209
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.61
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.08
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.60
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.73
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.67
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.72
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.75
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.71
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17815.43
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.14
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.64
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.89
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.46
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.99
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.88
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.25
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.52
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.47
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.38
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.30
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.16
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.01
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.07
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.05
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.25
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.84
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.70
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.33
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.81
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.81
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.67
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.27
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.05
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.86
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.10
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.06
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.36
 p-value of test no 179                :  9.0e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.71
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.59
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.39
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.92
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.55
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 219                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4660.69
 p-value of test no 222                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.82
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.32
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4366.45
 p-value of test no 228                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.55
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.71
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.30
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000341179
 
 Normal statistic for number of bits   :    2.70
 p-value of test no 232                :  3.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.64
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000035587
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:19.97
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206176274.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27817
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.42
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.52
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.07
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.95
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.93
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.87
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.97
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.71
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  182.26
 p-value of test no 54                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.87
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.62
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.87
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.49
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.59
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.64
 p-value of test no 66                 :  8.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.07
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.90
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908165
   j =  2                              :            45913
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46289
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870289
   j =  1                              :        399907422
   j =  2                              :            46289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 73                 :    0.9939
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.94
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.18
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.28
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.90
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.44
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.54
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.55
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.11
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.53
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.03
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.85
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.97
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.20
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.03
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.14
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.51
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.48
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.34
 p-value of test no 154                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.94
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.63
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.73
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.58
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.14
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.03
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.77
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.27
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.01
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.56
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.74
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.46
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.44
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.28
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.66
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.86
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.71
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.43
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.13
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.07
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.36
 p-value of test no 177                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.51
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.69
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.70
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.26
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.86
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9789.06
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.53
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.13
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.00
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.57
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.55
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.59
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.41
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999931460
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.93
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999932324
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.52
 p-value of test no 238                :    0.9941
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:36.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207093778.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27818
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.58
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.76
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.12
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.49
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.71
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.73
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.02
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.51
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.05
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.41
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.43
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.67
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908588
   j =  2                              :            45703
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908257
   j =  2                              :            45864
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 100                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -2.10e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.89
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.58
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.22
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.89
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.65
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.70
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.75
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.36
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.45
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17710.19
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.01
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.48
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.11
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.99
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.11
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.56
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.02
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.92
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.76
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.77
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.29
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.16
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.82
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.92
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.35
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.24
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.82
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.91
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.29
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.82
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.95
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.16
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.42
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.69
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.44
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.22
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.33
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.84
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.97
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.02
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.61
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.58
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.06
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.64
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.76
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.39
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.56
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.75
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.95
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.63
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.50
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000049987
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.48
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999933674
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9932
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:02.81
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208142354.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27819
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    4.50
 p-value of test no 24                 :  5.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     813
 p-value of test no 25                 :    0.9983
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.19
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.21
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.92
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.57
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.90
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.07
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.97
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.24
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.89
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.75
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.09
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.04
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.46
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908222
   j =  2                              :            45883
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.08
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.45
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.32
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.11
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.97
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.45
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.64
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.34
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.70
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17021.02
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.87
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.44
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.64
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.78
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.33
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.39
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.16
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.46
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.73
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.24
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.00
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.43
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.78
 p-value of test no 161                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.52
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.69
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.89
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.49
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.23
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.96
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.71
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.88
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.97
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.08
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.70
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.39
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.09
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.72
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    2.45
 p-value of test no 189                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.16
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.68
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.68
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.87
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.20
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.24
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.74
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.52
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.87
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.11
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.84
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.77
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999959633
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.35
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999944729
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 240                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:01:33.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209190930.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27820
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.62
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.30
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.79
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.18
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.45
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.01
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.13
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.53
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.90
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45701
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908600
   j =  2                              :            45697
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.29
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.31
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.58
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.31
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.19
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.75
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.70
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.33
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.02
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.97
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.72
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.11
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.23
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.44
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.26
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.55
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.20
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.82
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.64
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.92
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.67
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.05
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.27
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.61
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.40
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.28
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.21
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.09
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.53
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.60
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.98
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.21
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.25
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.74
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.05
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.95
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.63
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.62
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.79
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.23
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.04
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.84
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.02
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.99
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.07
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.78
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.42
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10273.76
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.28
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.38
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.05
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.97
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.61
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.55
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.99
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000037954
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.62
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000049447
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:21:21.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189497363.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27821
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 21                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.39
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    9.19
 p-value of test no 40                 :  3.8e-5    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.93
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.35
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.07
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.60
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.09
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.86
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.01
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.92
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.74
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.02
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.62
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.44
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45381
 p-value of test no 70                 :    0.9901
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869381
   j =  1                              :        399909241
   j =  2                              :            45375
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908378
   j =  2                              :            45805
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.74
 p-value of test no 115                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.40
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.50
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.84
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.01
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.44
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.24
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.16
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.13
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.56
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.11
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17503.15
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.69
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.75
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.02
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.93
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.74
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.15
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.14
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.12
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.51
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.04
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.16
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.87
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.35
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.01
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.75
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.80
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.04
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.15
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.73
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.84
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4813.36
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.56
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.66
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.67
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.04
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.05
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.00
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   32.57
 p-value of test no 176                :  1.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.97
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.90
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.10
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 206                :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  256.86
 p-value of test no 207                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.29
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.60
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.21
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.48
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.90
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.75
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.02
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.08
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.17
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000007132
 
 Normal statistic for number of bits   :   0.056
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.87
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999922109
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:30.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NP, t = 16           3.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190808083.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27822
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 9                  :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 38                 :    0.9989
 
 Stat. AD after spacings (mNP2-S)      :    4.65
 p-value of test no 39                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.58
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.70
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.65
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.05
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.53
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.88
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.00
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.91
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.87
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.34
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.48
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.12
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.09
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4811.09
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46253
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870253
   j =  1                              :        399907498
   j =  2                              :            46245
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46293
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870293
   j =  1                              :        399907418
   j =  2                              :            46285
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.91
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.94
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.95
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.00
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.33
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.29
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.46
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.46
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.08
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.73
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17351.22
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.11
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.57
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.44
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.28
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.80
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.09
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.85
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.20
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.60
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.27
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.32
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.45
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.78
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.10
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.15
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.25
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.07
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.91
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.89
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.41
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.85
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.35
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.76
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.04
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.05
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.68
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.67
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.68
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.89
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.21
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.98
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.22
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.59
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.58
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.70
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.70
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.20
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.78
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11556.12
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.88
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.63
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000118561
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.82
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999951326
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:22.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191856659.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27823
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.87
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.84
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.00
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.95
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.19
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.96
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.14
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.70
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6788.86
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.04
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.34
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.43
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.62
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.71
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908229
   j =  2                              :            45884
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908390
   j =  2                              :            45796
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 86                 :  7.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    4.75
 p-value of test no 88                 :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9941
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.02
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.56
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.25
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.17
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.46
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.21
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.69
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.70
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.18
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.059
 p-value of test no 134                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.93
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.55
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.12
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.88
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.70
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.45
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.73
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.33
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.31
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.42
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.90
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.08
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.82
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.07
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.63
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.34
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.04
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.80
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.99
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.63
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.42
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.12
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.13
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.55
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.38
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.69
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.19
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.88
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.81
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.87
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.55
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.96
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.51
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.92
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.21
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.90
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.37
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.64
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.95
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.59
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.15
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.52
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.62
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.95
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.25
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000079279
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.56
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999896756
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:03.18
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192675859.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27824
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4506
 p-value of test no 14                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.52
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.41
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.13
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.65
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.38
 p-value of test no 51                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.42
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.16
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.40
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.21
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1309.87
 p-value of test no 56                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7213.18
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.67
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.99
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.90
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.18
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908020
   j =  2                              :            45987
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908694
   j =  2                              :            45650
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  8.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
 p-value of test no 93                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  3.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.76
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.16
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.71
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.93
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.10
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.45
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.66
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.39
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.26
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.62
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17669.54
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.84
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.94
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.02
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.38
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.38
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.93
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.72
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.32
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.35
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.80
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.08
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.83
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.85
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.74
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.52
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.20
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.94
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.91
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.82
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.76
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.10
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.31
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.13
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.70
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.25
 p-value of test no 171                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.16
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.73
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.67
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.97
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.01
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 183                :    0.06
 
 Sample variance                       :    3.06
 p-value of test no 184                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.03
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.23
 p-value of test no 207                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.33
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.48
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.25
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.77
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.52
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.47
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.23
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.59
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12204.75
 p-value of test no 230                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.42
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000020827
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   94.27
 p-value of test no 233                :  5.7e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000076471
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:45.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193658899.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27825
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7534
 p-value of test no 21                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.15
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.48
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.54
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.76
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.21
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.11
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.02
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.63
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.57
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.86
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.53
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.45
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.51
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5208.74
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45866
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908269
   j =  2                              :            45864
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 98                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 99                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-5
 p-value of test no 112                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.02
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.10
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.05
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.41
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.29
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.25
 p-value of test no 129                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.29
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.97
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.41
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.04
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.01
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.50
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.66
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.13
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.21
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.67
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.76
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.90
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.11
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.75
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.51
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.60
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.34
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.10
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.14
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.13
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.44
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.56
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.88
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.34
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.83
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.49
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.28
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.46
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4807.38
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.86
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.26
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.58
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.50
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.75
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.21
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.01
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.44
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.23e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.33
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.94
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.56
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3907.20
 p-value of test no 228                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.59
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.86
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999972311
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.03
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000005494
 
 Normal statistic for number of bits   :   0.043
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.40e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:55.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195100691.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27826
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 7                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4185
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.99
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.97
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.52
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.00
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.29
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.74
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.30
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7255.91
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.48
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.98
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.39
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.66
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.55
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908266
   j =  2                              :            45861
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45463
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869463
   j =  1                              :        399909079
   j =  2                              :            45453
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.34e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.82
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.03
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.93
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.15
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.45
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.41
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.64
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.17
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.65
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.07
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.00
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.54
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.33
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.13
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.44
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.34
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.33
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.31
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.85
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.75
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.32
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.82
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.54
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.69
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.91
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.05
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.81
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.36
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.16
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.38
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.81
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.67
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.10
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.81
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.44
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.01
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.40
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.36
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.91
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.07
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.84
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.13
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.82
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.64
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.23
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.32
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12134.92
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.04
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999947918
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.98
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000093331
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
 p-value of test no 241                :    0.9985
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:08.05
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196116499.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27827
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.10
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.43
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.72
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.67
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.79
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.13
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.51
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.60
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.35
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.92
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.69
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.57
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.67
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.49
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.40
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.25
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908262
   j =  2                              :            45866
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908005
   j =  2                              :            45993
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-4
 p-value of test no 110                :  2.6e-3
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  107.36
 p-value of test no 119                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.53
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.30
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.01
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.94
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.43
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.81
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.39
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.87
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17474.10
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.75
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.95
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.21
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.42
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.58
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.23
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.32
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.77
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.05
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.16
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.59
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.06
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.60
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.54
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.74
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.53
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.01
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.39
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.62
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.24
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.33
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.35
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.74
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.25
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.69
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.11
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.72
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.35
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.00
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.88
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.32
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.85
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.90
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4710.95
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.14
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.80
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.84
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.79
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.34
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000100375
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.84
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999977729
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:36.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197132307.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27828
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.75
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.44
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.77
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.03
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.97
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.26
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.29
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.45
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1341.11
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.87
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.92
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.05
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.36
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.43
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5231.13
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908475
   j =  2                              :            45755
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908612
   j =  2                              :            45688
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.76
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.39
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.93
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.98
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.91
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.36
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.31
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.77
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.58
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.94
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17341.66
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.94
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.30
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.48
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.72
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.06
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.16
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.28
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.35
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.33
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.68
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.05
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.87
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.87
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.76
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.21
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.93
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.77
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.06
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.01
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.87
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.82
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.77
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.14
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.49
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.94
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.53
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.82
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.21
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.68
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.83
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.83
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.49
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.17
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.17
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.04
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11453.83
 p-value of test no 229                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.11
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.14
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000036604
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.00
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000011161
 
 Normal statistic for number of bits   :   0.088
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    2.14
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.012
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:57.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198082579.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27829
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.33
 p-value of test no 34                 :  2.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.81
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.74
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.82
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.40
 p-value of test no 50                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.77
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.73
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.28
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.59
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  497.09
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.37
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.60
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.30
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.41
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.50
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.13
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5192.66
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45462
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869462
   j =  1                              :        399909079
   j =  2                              :            45456
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908379
   j =  2                              :            45800
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.42
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.39
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.19
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.18
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.38
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.87
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.92
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.02
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.62
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.03
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.78
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.94
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.22
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.79
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.24
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.87
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.29
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.48
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.67
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.71
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.82
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.07
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.85
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.20
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.78
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.85
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.07
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.79
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.56
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.59
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.40
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.15
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.34
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.04
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.02
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.38
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.39
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.88
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.01
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.49
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 214                :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10387.79
 p-value of test no 215                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4698.01
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.25
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.87
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.09
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.91
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.49
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.24
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999955463
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.98
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000003811
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:35.68
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199098387.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27830
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 9                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1230
 p-value of test no 11                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334350
   j =  1                              :        599997540
   j =  2                              :             1230
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.49
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.19
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.89
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.10
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.08
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.75
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.12
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7181.62
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.50
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.48
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.15
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.54
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45493
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869493
   j =  1                              :        399909016
   j =  2                              :            45489
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908427
   j =  2                              :            45785
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.81
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.47
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.23
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.94
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.68
 p-value of test no 123                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.75
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.73
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.15
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.89
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.77
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17199.10
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.65
 p-value of test no 146                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.01
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.82
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.94
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.56
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.67
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.10
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.70
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.91
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.86
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.32
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.12
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.13
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.50
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.51
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.61
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.77
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.87
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.83
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.31
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.92
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.68
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.71
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.13
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.82
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.46
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.59
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.48
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.81
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.40
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.87
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.56
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.78
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.74
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.56
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.74
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.03
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.67
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.89
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.52
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.49
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000129001
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.99
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999925505
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    2.41
 p-value of test no 249                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    2.19
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:14.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9990 
  11  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200245267.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27831
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.90
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.77
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.04
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.96
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.47
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.95
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.48
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.64
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.51
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.02
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.00
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.80
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.81
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.09
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.44
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4838.62
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908749
   j =  2                              :            45621
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907950
   j =  2                              :            46022
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.92
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.91
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.97
 p-value of test no 123                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.73
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.09
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.56
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.71
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.86
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.83
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.28
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.82
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.06
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.74
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.24
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.17
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.36
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.25
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.38
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.18
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.62
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.30
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.94
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.73
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.91
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.23
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.97
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.57
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.62
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.57
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.94
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.05
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.91
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4731.27
 p-value of test no 173                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.26
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.09
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.04
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.62
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.81
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.91
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.35
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.92
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.74
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.12
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.81
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.21
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.67
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12065.83
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.90
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000146251
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.12
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999923843
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 8.88e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.11
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201228307.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27832
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5259
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.24
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.30
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.41
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.50
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.74
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.19
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.81
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.58
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.94
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.04
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.27
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.29
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4837.60
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908398
   j =  2                              :            45795
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908673
   j =  2                              :            45656
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.50
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.87
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.43
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.61
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.32
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.31
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.73
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.10
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.02
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17459.07
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.28
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.52
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.71
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.50
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.25
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.16
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.61
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.70
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.59
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.31
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.91
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.95
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.98
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.01
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.67
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.56
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.20
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.05
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.30
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.68
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.66
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.43
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.51
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.08
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.56
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.25
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.70
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.59
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.31
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.80
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.36
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.40
 p-value of test no 198                :    0.9942
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.81
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.49
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.65
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.00
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.79
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.14
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.86
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.62
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.00
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.80
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.40
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000044569
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.53
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000089398
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:06.67
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202178579.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27833
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7090
 p-value of test no 20                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9928
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.57
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.31
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.68
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.13
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.47
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.54
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.45
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.90
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.02
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.14
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.99
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.83
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.28
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.40
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908178
   j =  2                              :            45905
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45549
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869549
   j =  1                              :        399908907
   j =  2                              :            45539
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 108                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.20
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.11
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.61
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.70
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.76
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.15
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.99
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.14
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.41
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.94
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.76
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.22
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.93
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.70
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.73
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.62
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.52
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.82
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.14
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.99
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.47
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.29
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.81
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.82
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.48
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.42
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.81
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.38
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.67
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.24
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.33
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.01
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.92
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.94
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.96
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.39
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.96
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.91
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.08
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.57
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.14
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.30
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.19
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.23
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.37
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 212                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9715.47
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.16
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.06
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.87
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.20
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12144.72
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.94
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.42
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000008152
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.36
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999936917
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.17
 p-value of test no 254                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:08.86
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203325459.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27834
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4531
 p-value of test no 14                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.76
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.30
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.84
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.60
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.25
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.64
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.38
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.32
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6796.12
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.97
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.69
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.23
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.47
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.45
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908038
   j =  2                              :            45978
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908469
   j =  2                              :            45761
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.50
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.83
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.85
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.57
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.48
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.91
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.88
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.65
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17070.13
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.32
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.68
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.84
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.30
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.06
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.29
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.11
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.16
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.63
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.46
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.03
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.37
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.20
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.39
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.47
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.97
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.90
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.12
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.16
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.82
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.70
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.53
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.82
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.71
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.60
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.17
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.71
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.21
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.32
 p-value of test no 176                :    0.9987
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :   0.099
 p-value of test no 184                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.57
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.82
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.60
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.18
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.33
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.12
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4699.75
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.81
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.75
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.39
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.51
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.19
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000083125
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.65
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000145663
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:04.43
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204308499.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27835
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 9                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997199
   j =  2                              :             1399
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.14
 p-value of test no 28                 :    0.9991    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.60
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.19
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.95
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.79
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.34
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.93
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.06
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.47
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.20
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 64                 :  9.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.46
 p-value of test no 65                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.12
 p-value of test no 66                 :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.82
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.28
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45468
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869468
   j =  1                              :        399909066
   j =  2                              :            45464
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907949
   j =  2                              :            46024
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.45
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.20
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.05
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.52
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.80
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.23
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.82
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.94
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
 p-value of test no 138                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.94
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17207.16
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.33
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.00
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.38
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.93
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.02
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.48
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.16
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.49
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.46
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.53
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.84
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.35
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.16
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.83
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.23
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.45
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.23
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.26
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.32
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.14
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.17
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.08
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.95
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.81
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.74
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.61
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.60
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.13
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.24
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.36
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.25
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.73
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.95
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.33
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.35
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10366.35
 p-value of test no 215                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5058.98
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.01
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3915.68
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.12
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12041.55
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.87
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.16
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000020230
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.69
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999907139
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 236                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:31.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NP, t = 5            0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205258771.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27836
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7540
 p-value of test no 18                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.78
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.18
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.51
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.70
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.68
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.65
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.10
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.52
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.35
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.33
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.17
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.33
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.53
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908029
   j =  2                              :            45981
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908815
   j =  2                              :            45588
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  6.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
 p-value of test no 79                 :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.95
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.62
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.99
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.33
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.52
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.37
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.07
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.18
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.42
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.60
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.37
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.77
 p-value of test no 146                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.93
 p-value of test no 147                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.30
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.25
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.54
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.33
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.86
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.44
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.47
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.33
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.99
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.67
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.69
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.77
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.51
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.51
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.62
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.69
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.85
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.98
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.99
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.95
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.75
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.86
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.42
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.60
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  443.54
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.13
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.16
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    2.17
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.69
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.33
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.01
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.76
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.71
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.52
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.38
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.89
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.53
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.45
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.61
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000106246
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.66
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999907436
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 238                :  6.5e-3
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:51.72
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206274579.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27837
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.98
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.07
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.59
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.73
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.50
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.80
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.17
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.38
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.60
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.68
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.65
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908650
   j =  2                              :            45669
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907814
   j =  2                              :            46090
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.00
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.77
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.58
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.47
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.90
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.64
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 130                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.15
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.65
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.38
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.22
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.07
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.04
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.70
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.72
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.30
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.95
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.02
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.08
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.92
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.04
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.88
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.07
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.44
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.81
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.25
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.22
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.34
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.73
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.26
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.07
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.48
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.33
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.83
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.10
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.45
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   30.35
 p-value of test no 176                :  2.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.31
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.11
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.00
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.19
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.89
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.60
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.09
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.69
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.77
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.98
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11469.83
 p-value of test no 229                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.74
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.81
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999893642
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.47
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999975146
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:46.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207257619.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27838
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.63
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.40
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.67
 p-value of test no 48                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.06
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.89
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.44
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.21
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.02
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.96
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.26
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 59                 :    0.9960
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.57
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.47
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.36
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.26
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908194
   j =  2                              :            45897
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.09
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.81
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.42
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.97
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.98
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.21
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.05
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.27
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.13
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.54
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.93
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.30
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.28
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.72
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.86
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.92
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.92
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.48
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.54
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.41
 p-value of test no 160                :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.00
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.71
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.10
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.88
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.59
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.98
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.71
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  307.62
 p-value of test no 169                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.11
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.29
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.19
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.20
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.48
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.96
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.86
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.52
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.19
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.41
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.14
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.73
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.60
 p-value of test no 218                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.63
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.38
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.49
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.97
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11606.71
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.42
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   88.61
 p-value of test no 231                :  2.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999888374
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.65
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000080992
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:44.07
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208470035.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27839
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7574
 p-value of test no 18                 :  1.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.49
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.82
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.53
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.25
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.46
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.89
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.58
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.93
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.46
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.95
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.15
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5090.05
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907777
   j =  2                              :            46101
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46214
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870214
   j =  1                              :        399907575
   j =  2                              :            46208
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.41
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.19
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.19
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.31
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.54
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.08
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.79
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.93
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.39
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.70
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.46
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.72
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.80
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.82
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.12
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.00
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.10
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.10
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.18
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.17
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.12
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.40
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.01
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.19
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.65
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.60
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.82
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.70
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.77
 p-value of test no 165                :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.41
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.03
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.71
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.54
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.67
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.33
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.45
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.92
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.39
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.69
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.34
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.23
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.22
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.38
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10193.23
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.73
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.16
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.43
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.20
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.80
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.32
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.48
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.84
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000110566
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.21
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000174526
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 241                :    0.9917
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:59:20.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209485843.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27840
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 12                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.70
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.73
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.10
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.17
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.19
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.76
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.58
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.11
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.11
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.99
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.64
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.66
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.25
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.13
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908072
   j =  2                              :            45964
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908006
   j =  2                              :            45994
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 80                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.84
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.27
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.24
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.91
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.25
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.93
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.34
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.19
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17652.94
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.01
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.03
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.35
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.19
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.71
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.53
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.56
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.64
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.77
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.02
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.91
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.60
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.31
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.37
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.80
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.59
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.78
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.28
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.32
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.74
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.97
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5193.88
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.13
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.62
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.81
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.54
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.72
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.24
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.84
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.89
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.30
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.46
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.79
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.58
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.11
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.95
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.54
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.30
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.63
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.02
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.64
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000112948
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.83
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999906092
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:57.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189530132.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27841
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.33
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    4.03
 p-value of test no 44                 :  8.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.09
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.79
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.38
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.64
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.58
 p-value of test no 53                 :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.20
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.65
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.14
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.59
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.22
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.52
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.46
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.44
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908448
   j =  2                              :            45767
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907968
   j =  2                              :            46013
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.99
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.33
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.75
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.91
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.86
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.83
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.70
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.14
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.27
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.80
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.86
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.34
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.46
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.73
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.14
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.52
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.34
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.96
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.47
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.61
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.77
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.91
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.96
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.59
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.74
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.71
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.30
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.80
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.58
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.07
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.42
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.21
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.26
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.86
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.45
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.32
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.12
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.53
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.51
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.36
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.81
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.88
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.23
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.34
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.73
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.35
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.23
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.29
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.98
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000002605
 
 Normal statistic for number of bits   :   0.021
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.15
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000015487
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    2.40
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    2.03
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:54.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190677012.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27842
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.69
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.62
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.79
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.43
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.38
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.44
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.77
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.57
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.76
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.30
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.19
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.80
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908477
   j =  2                              :            45757
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908693
   j =  2                              :            45649
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.12
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.66
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.57
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.47
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.88
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.77
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.71
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.15
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.93
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 142                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17785.51
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.32
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.23
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.12
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.07
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.09
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.50
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.74
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.07
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.53
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.68
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.13
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.37
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.75
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.58
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.57
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.46
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.52
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.63
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.94
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.64
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.67
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.50
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.83
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.36
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.65
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.58
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.79
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.54
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.20
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.19
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.62
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.39
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.92
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.41
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.46
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.28
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.96
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.24
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999760106
 
 Normal statistic for number of bits   :   -1.90
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.41
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000208507
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9979
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.090
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:57.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191430676.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27843
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7041
 p-value of test no 20                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.82
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.07
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.71
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.13
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.34
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.57
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.86
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.66
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1319.46
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.54
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.37
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.30
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.77
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.02
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45310
 p-value of test no 70                 :    0.9961
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869310
   j =  1                              :        399909381
   j =  2                              :            45308
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908337
   j =  2                              :            45824
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.78
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.52
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.01
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.89
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.24
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.79
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.55
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.10
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.09
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.66
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.56
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.99
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.88
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.58
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.81
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.20
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.06
 p-value of test no 155                :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.72
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.70
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.75
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.12
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.80
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.09
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.17
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.47
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.04
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.68
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.89
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.77
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.25
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.22
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.18
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.62
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.43
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.42
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.73
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.79
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.02
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.88
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.86
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.83
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.85
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.42
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.72
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.11
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3938.32
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.31
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.06
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000094798
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.08
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999957728
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:18.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192348180.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27844
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 12                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.25
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.58
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.77
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.78
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.91
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.71
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.25
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.01
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.64
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.99
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.43
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.56
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.45
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.28
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.90
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908129
   j =  2                              :            45928
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908630
   j =  2                              :            45682
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 92                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.89
 p-value of test no 119                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.34
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.03
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.12
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.13
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.26
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.96
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.75
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.12
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.66
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17662.15
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.15
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.61
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.67
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.58
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.23
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.62
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.10
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.01
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.71
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.39
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.00
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.39
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.63
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.52
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.86
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.63
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.65
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.07
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.01
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.65
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.61
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.01
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.78
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.41
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.94
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.59
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.48
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.10
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.66
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.81
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.57
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.74
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.16
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.36
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.33
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.15
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 209                :    0.9912
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.84
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10193.96
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.15
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.11
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.25
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.18
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.86
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.70
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.63
 p-value of test no 231                :  6.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999959852
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.35
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000017008
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:19.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193593364.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27845
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.60
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.86
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.77
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.78
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.02
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.12
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.26
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.80
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6761.61
 p-value of test no 57                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.03
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.63
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.04
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.71
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.09
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908433
   j =  2                              :            45782
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908578
   j =  2                              :            45702
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.50
 p-value of test no 115                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.86
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.09
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.44
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.46
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.81
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.57
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.07
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.59
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.65
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.69
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.66
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.49
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.69
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.37
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.06
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.00
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.21
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.29
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.12
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.01
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.57
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.36
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.63
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.22
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.48
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.18
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.16
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.60
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.58
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.12
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.46
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.39
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.07
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.80
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.37
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.64
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.78
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.98
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.90
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 202                :  6.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.77
 p-value of test no 203                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.30
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.72
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.17
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.62e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.07
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.60
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.67
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.52
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.62
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.44
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.83
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999873812
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.06
 p-value of test no 233                :  4.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000219865
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:24.57
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194543636.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27846
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9944
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    3.00
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     349
 p-value of test no 37                 :  3.1e-3
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.71
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.86
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.35
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.74
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.89
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.00
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.61
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.30
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.68
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.61
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.80
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908119
   j =  2                              :            45936
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907888
   j =  2                              :            46056
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  3.9e-3
 
 Anderson-Darling statistic = A2       :    5.06
 p-value of test no 95                 :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  8.8e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.28
 p-value of test no 116                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.82
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.07
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.46
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.62
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.27
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.91
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17613.85
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.79
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.83
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.03
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.48
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.83
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.68
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.99
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.06
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.90
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.80
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.41
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.46
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.21
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.01
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.26
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.60
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.49
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.64
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.30
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.82
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.03
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.35
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.02
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.30
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.74
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.11
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.85
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.12
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.31
 p-value of test no 177                :  4.7e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.70
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.27
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.60
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.46
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.05
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.46
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.11
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.35
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.56
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.86
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.81
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.16
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.87
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999844703
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.26
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999991754
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:38.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  8.8e-4
  56  SampleCorr, k = 2               0.9995 
  80  LinearComp, r = 0               4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195657748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27847
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.88
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.54
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.31
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.70
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.73
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.34
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.79
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.72
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.34
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.83
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.20
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.07
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.88
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.08
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908822
   j =  2                              :            45580
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907954
   j =  2                              :            46020
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-3
 p-value of test no 91                 :    0.9982
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.24
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.85
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.44
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.90
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.22
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.74
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.13
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.88
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.48
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.15
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.44
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.95
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.17
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.21
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.62
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.00
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.15
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.33
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.84
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.07
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.63
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.66
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.31
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.49
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.86
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.47
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.37
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.97
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.31
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.97
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.27
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.05
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.09
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.64
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.98
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.68
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.85
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.72
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.42
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.11
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.86
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.86
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.68
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.24
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.43
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.80
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.34
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.20
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.90
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.09
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.00
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.60
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000088408
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.19
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999856961
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9936
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:02.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196542484.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27848
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 7                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.10
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.71
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.67
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.82
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.74
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.41
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.36
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.67
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.82
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.97
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.76
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.56
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.50
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46258
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870258
   j =  1                              :        399907487
   j =  2                              :            46252
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908691
   j =  2                              :            45647
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.39
 p-value of test no 119                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.05
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.35
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.48
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.18
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.10
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.82
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.00
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.17
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.12
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.61
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.49
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.05
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.33
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.29
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.32
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.80
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.62
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.00
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.47
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.99
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.38
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.01
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.67
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.22
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.28
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  306.88
 p-value of test no 166                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.73
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.42
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.80
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.59
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.37
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.97
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.79
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.86
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.94
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.87
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.77
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.60
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10341.30
 p-value of test no 211                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.53
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.34
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.64
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4318.88
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.82
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.20
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.08
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.71
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000019318
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.40
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000147697
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:45.98
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197623828.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27849
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.99
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.45
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.24
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.36
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.59
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.83
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.68
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.97
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.71
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.54
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.24
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.00
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908416
   j =  2                              :            45789
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908134
   j =  2                              :            45927
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.17
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.41
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.49
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.68
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.52
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.31
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.42
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.19
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.60
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.78
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.98
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.86
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.64
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.63
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.00
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.46
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.48
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.51
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.68
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.98
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.80
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.79
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.57
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.65
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.09
 p-value of test no 165                :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.97
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.61
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.93
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.16
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.35
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.52
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.71
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.76
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.08
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.29
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.52
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.66
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.76
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
 p-value of test no 186                :    0.9986
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 188                :    0.9901
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.08
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.80
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.82
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.74
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.37
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.65
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.76
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.70
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.78
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.21
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.97
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000007210
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.09
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999986990
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    2.13
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:15.80
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198606868.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27850
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    4.82
 p-value of test no 39                 :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.34
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.51
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.20
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.90
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.33
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.36
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.53
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.87
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.53
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.84
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.96
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.40
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.85
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908263
   j =  2                              :            45864
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908336
   j =  2                              :            45829
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.79e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.01
 p-value of test no 116                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.50
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.55
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.85
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.17
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.60
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.06
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.85
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.76
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.32
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17658.39
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.58
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.46
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.40
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.53
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.58
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.68
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.35
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.89
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.51
 p-value of test no 160                :  4.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.95
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.24
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.28
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.68
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.41
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.86
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.29
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.23
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.97
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.21
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.51
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.10
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.18
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.51
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.65
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.43
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.53
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.91
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.69
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.42
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.61
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.62
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.75e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.21
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.26
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.67
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.41
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.02
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.05
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.70
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999964628
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.39
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000016273
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:42.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199655444.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27851
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.91
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.33
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.71
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.89
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.11
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.57
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.39
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.93
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.82
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.83
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.28
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908184
   j =  2                              :            45902
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907899
   j =  2                              :            46043
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.89
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.11
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.73
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.05
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.31
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.86
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.81
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.24
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.24
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.62
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.29
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.13
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.65
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.37
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.66
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.81
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.91
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.02
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.65
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.10
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.54
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.57
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.36
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.51
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.57
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.73
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.50
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.54
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.59
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.57
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.22
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.51
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.48
 p-value of test no 170                :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.90
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.50
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.27
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.21
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.18
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.67
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.68
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.86
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.61
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.28
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 208                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9698.95
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.04
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5063.27
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.70
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.63
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.11
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.24
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.95
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.78
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000086749
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.53
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000032860
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:07.01
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200671252.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27852
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9946
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.71
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.51
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.44
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.46
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.44
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.97
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1564.83
 p-value of test no 56                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.77
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.63
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.03
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.89
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.90
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.68
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908149
   j =  2                              :            45921
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908499
   j =  2                              :            45749
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 91                 :    0.9958
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.97
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.12
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.31
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.96
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.98
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.51
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.59
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.20
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.13
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17728.11
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.56
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.32
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.30
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.26
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.05
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.06
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.10
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.37
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.15
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.63
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.08
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.52
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.00
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.14
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.76
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.44
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.07
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.85
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.29
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.28
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.18
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.14
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.88
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.54
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.53
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.79
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.15
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.55
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.48
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 201                :    0.9954
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.79
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.73
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.69
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.46
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.45
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.97
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.30
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3906.48
 p-value of test no 228                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.71
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.56
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.18
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000119776
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.24
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000112807
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:30.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201818132.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27853
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    3.66
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    3.78
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     185
 p-value of test no 43                 :  3.2e-3
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.81
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.02
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.59
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.98
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.51
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.00
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.23
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.33
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6827.78
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.10
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.37
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.25
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.63
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45506
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869506
   j =  1                              :        399908989
   j =  2                              :            45504
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908141
   j =  2                              :            45922
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.92
 p-value of test no 88                 :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  2.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.83
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.10
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.43
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.92
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.45
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.81
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.40
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.10
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.18
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.40
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.56
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.26
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.28
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.22
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.75
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.10
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.01
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.01
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.40
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.05
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.80
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.52
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.21
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.31
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.22
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.71
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.29
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.87
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.68
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.37
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.63
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.88
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.37
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.54
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.49
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.53
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.12
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.08
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.14
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.78
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.19
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.64
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.20
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.98
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.00
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.20
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.68
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.88
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 223                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.98
 p-value of test no 226                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.11
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.00
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.29
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12138.61
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.89
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999938696
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.01
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000198868
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:07.98
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202866708.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27854
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4180
 p-value of test no 14                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    3.78
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    4.34
 p-value of test no 32                 :  6.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.39
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.43
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.56
 p-value of test no 52                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.23
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.03
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.70
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.89
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.93
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.30
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.24
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.99
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.69
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907877
   j =  2                              :            46057
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907841
   j =  2                              :            46078
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-3
 p-value of test no 106                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 107                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.30
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.56
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.26
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.67
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.86
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.95
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.95
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.98
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.90
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.83
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17212.83
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.83
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.84
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.02
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.92
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.26
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.19
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.86
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.79
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.03
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.83
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.00
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.33
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.38
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.00
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.23
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.81
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.44
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.18
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.76
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.44
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5279.70
 p-value of test no 168                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.64
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.89
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.82
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.64
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.41
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.76
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.58
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.14
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.99
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.11
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.42
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9770.19
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.64
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.20
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.50
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.19
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.84
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.62
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.18
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000008617
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.36
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999968699
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:20.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203849748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27855
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 12                 :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    3.46
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.66
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.73
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.72
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.56
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.30
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.62
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.53
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.79
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.53
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.96
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.95
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.42
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.16
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.30
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908361
   j =  2                              :            45812
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45566
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869566
   j =  1                              :        399908870
   j =  2                              :            45562
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 92                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.23
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.92
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.36
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.70
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.42
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.29
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.81
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.10
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.46
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.65
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.80
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.86
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.54
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.56
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.16
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.39
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.36
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.52
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.67
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.58
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.93
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.82
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.53
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.05
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.18
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.15
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.07
 p-value of test no 166                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.44
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.46
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.83
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.59
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.56
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.11
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.43
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.88
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.71
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.29
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.23
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.93
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 210                :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.55
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 212                :  5.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    6.35
 p-value of test no 214                :  7.3e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9570.88
 p-value of test no 215                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.14
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.05
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.49
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.05
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.05
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.94
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.64
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000034732
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.22
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999979721
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 235                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9956
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.58e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:50.65
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204832788.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27856
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     975
 p-value of test no 25                 :  7.0e-3
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    7.55
 p-value of test no 32                 :  1.9e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.25
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.24
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.05
 p-value of test no 51                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.36
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.14
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.05
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.60
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.32
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.11
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.93
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.41
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.28
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.16
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908393
   j =  2                              :            45799
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907853
   j =  2                              :            46066
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.83
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.36
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.25
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.52
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.78
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.03
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.89
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 126                :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.88
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.93
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.10
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.45
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.04
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.30
 p-value of test no 147                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.84
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.35
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.53
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.34
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.02
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.45
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.55
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.24
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.14
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.45
 p-value of test no 160                :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.49
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.61
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.19
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.94
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.26
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.91
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.45
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.29
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.35
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.42
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.85
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.19
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.48
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.01
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.27
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.33
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.06
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.97
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.32
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.25
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.59
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.43
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.36
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.29
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.02
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.47
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999989411
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999995891
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:20.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205881364.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27857
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    3.77
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.33
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.56
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.17
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.04
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.03
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.35
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.94
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1534.95
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.19
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 59                 :    0.9903
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.53
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.72
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.45
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4888.50
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907894
   j =  2                              :            46047
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908096
   j =  2                              :            45949
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 84                 :    0.9952
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.60
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.78
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.09
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.68
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.90
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.10
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.74
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.71
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.33
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.56
 p-value of test no 134                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.08
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.78
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.70
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.95
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.04
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.11
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.98
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.32
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.35
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.78
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.93
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.22
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.58
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.07
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.01
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.24
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.18
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.42
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.04
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.21
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.13
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.14
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.68
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.19
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.30
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.25
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.09
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.21
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.94
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.97
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.98
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.57
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.29
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.76
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.70
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.13
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.05
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.71
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.39
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.34
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.25
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.07
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999925991
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.47
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000010564
 
 Normal statistic for number of bits   :   0.084
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9957
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:03.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               5.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207028244.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27858
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 6                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.64
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.37
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.52
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.11
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.86
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.22
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.00
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.67
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.28
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.51
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.97
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.99
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.77
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45539
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908926
   j =  2                              :            45531
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907647
   j =  2                              :            46175
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 92                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-6
 p-value of test no 109                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.03
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.62
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.52
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.58
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.56
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.21
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.72
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.61
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.67
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.72
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.27
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.47
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.35
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.56
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.60
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.35
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.43
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.74
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.11
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.96
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.38
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.61
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.78
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.69
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.57
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.75
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.29
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.48
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.75
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.49
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.97
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.70
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.14
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.01
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.03
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.07
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.43
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.50
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.91
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.58
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.82
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.11
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.39
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5151.96
 p-value of test no 226                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.69
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.34
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.67
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11499.96
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.82
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000103273
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.73
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000006229
 
 Normal statistic for number of bits   :   0.049
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:13.80
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208044052.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27859
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    3.16
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    3.25
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.72
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.25
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.46
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.43
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.51
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.22
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.96
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.36
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.69
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5117.05
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46226
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870226
   j =  1                              :        399907553
   j =  2                              :            46216
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907890
   j =  2                              :            46049
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.36
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.38
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.79
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.35
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.28
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.00
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.18
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.28
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.37
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.88
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.61
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.50
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.52
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.44
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.93
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.16
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.32
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.61
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.78
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.34
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.54
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.58
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.41
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.39
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.58
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.69
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.18
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.17
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.22
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.22
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  451.09
 p-value of test no 169                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.85
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.92
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.81
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.43
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.38
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.89
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.20
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9904
 
 Tests on the sum of all N observations
 Standardized normal statistic         :1.40e-16
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.52
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.91
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.25
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.05
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.39
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.93
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.43
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4287.23
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.94
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.60
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.41
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000064357
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.06
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999968054
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.97
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:02.27
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209059860.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27860
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 4                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7528
 p-value of test no 18                 :  7.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 24                 :    0.9993    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.94
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.12
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.61
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.64
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.97
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.92
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.30
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.31
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.59
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.36
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.28
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.58
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.02
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.54
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45667
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869667
   j =  1                              :        399908671
   j =  2                              :            45657
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-5
 p-value of test no 113                :    0.9936
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  110.43
 p-value of test no 119                :  6.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.63
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.40
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.07
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.29
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.60
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.54
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.40
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.32
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17441.00
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.88
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.22
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.86
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.06
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.01
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.51
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.83
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.59
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.06
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.77
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.38
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.09
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.82
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.60
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.99
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.69
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.74
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.22
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.67
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.76
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.23
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.66
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.44
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.52
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.04
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.03
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.91
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   24.27
 p-value of test no 198                :  2.1e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.46
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.51
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.12
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.74
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.73
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.29
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.79
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.35
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.36
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.03
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.95
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999948056
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.82
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000091315
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:18:00.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          0.9993 
  59  WeightDistrib, r = 0            6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189562901.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27861
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.56
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.59
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.56
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.42
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.62
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.75
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.56
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.10
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.35
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.38
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   21.39
 p-value of test no 66                 :  6.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.61
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.34
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908294
   j =  2                              :            45844
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908836
   j =  2                              :            45573
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.52
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.18
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.74
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.62
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.42
 p-value of test no 124                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   58.83
 p-value of test no 125                :  8.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.61
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.30
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.16
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.56
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.11
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.69
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.77
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.00
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.98
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.30
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.17
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.48
 p-value of test no 154                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.54
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.57
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.81
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.01
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.14
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.82
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.64
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.00
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.58
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.88
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.08
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.47
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.16
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.97
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.88
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.32
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.97
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.88
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.82
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.47
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    1.96
 p-value of test no 176                :    0.9995    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.71
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.31
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.28
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.78
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.03
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.91
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.36
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.80
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.55
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.95
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.52
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.70
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.75
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.66
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999930548
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.33
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000036826
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:31.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              6.8e-4
  65  SumCollector                    8.6e-4
  80  LinearComp, r = 0               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190742549.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27862
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    3.38
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.59
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.05
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.39
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.59
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.27
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.10
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.83
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.97
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.01
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.07
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.45
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.91
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.23
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.09
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.82
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908646
   j =  2                              :            45671
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907892
   j =  2                              :            46051
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  8.8e-3
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.38
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.76
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.63
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.59
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.77
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.04
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.63
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.89
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.52
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17007.81
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.11
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.78
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.96
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.77
 p-value of test no 149                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.89
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.57
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.93
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.98
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.36
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.78
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.01
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.36
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.81
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.57
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.84
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.47
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.77
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.05
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.56
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.91
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.68
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.00
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.02
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4754.15
 p-value of test no 173                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.04
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.03
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.32
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    2.98
 p-value of test no 189                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.78
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.50
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.85
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.34
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.66
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.47
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.37
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.67
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.26
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.49
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.94
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000004915
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.37
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000083974
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:03.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191299610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27863
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     831
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.76
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.72
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.14
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.08
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.83
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.02
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.83
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6847.44
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.32
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.76
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.45
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5239.19
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908260
   j =  2                              :            45864
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.95
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.82
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.12
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.48
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.86
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.95
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.69
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.98
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.58
 p-value of test no 136                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.85
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.25
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.52
 p-value of test no 146                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.29
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.35
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.81
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.85
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.18
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.36
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.22
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.71
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.63
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.22
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.75
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.90
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.96
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.95
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.06
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.68
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.98
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.89
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.28
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.59
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.41
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.01
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.59
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.98
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.97
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.62
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.72
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    2.21
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.90
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.01
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.96
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.72
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.68
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.02
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4687.54
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.03
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.79
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.33
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.75
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.79
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.13
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999889520
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.42
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999958754
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 238                :  4.9e-3
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.96e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:15:53.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192249882.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27864
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.11
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.44
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.09
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.20
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.45
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  380.00
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.50
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.03
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.28
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.06
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.65
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.48
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.78
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908452
   j =  2                              :            45765
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45348
 p-value of test no 71                 :    0.9935
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869348
   j =  1                              :        399909307
   j =  2                              :            45342
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 103                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 116                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.13
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.76
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.31
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.40
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-4
 p-value of test no 127                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.48
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.26
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.51
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.77
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.97
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.15
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.04
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.83
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.87
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.38
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.89
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.39
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.45
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.91
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.13
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.87
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.13
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.52
 p-value of test no 162                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.96
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.59
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.53
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.77
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.20
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.18
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.94
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.35
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.88
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.39
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.64
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.66
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.16
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.81
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.23
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.37
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.09
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.98
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.80
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.47
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.15
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.82
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.33
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12161.38
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12210.30
 p-value of test no 230                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.31
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999866651
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.25
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000165100
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 241                :    0.9938
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:37.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193986586.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27865
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.42
 p-value of test no 29                 :  5.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.96
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.52
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.55
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.98
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.11
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.69
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.81
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7221.86
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.79
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.47
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.22
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5188.44
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907799
   j =  2                              :            46099
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908403
   j =  2                              :            45794
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 76                 :  5.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.54
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.69
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.43
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.64
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.97
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.94
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.57
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.60
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.80
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.07
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.66
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.82
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.66
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.86
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.46
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.64
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.03
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.76
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.38
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.11
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.46
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.05
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.80
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.47
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.81
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.22
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.03
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.83
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.38
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.41
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.22
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.81
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.41
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.88
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.55
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.13
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.60
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.28
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.12
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.33
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.74
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.97
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.03
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.60
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.72
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.97
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.72
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.45
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.52
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.11
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000105673
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.19
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999996770
 
 Normal statistic for number of bits   :  -0.026
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:23.78
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195002394.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27866
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4498
 p-value of test no 16                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.36
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.57
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.01
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.39
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.87
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.47
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.02
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.28
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.30
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.90
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.07
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.55
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.86
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.52
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.65
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908421
   j =  2                              :            45785
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908050
   j =  2                              :            45969
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.73
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.71
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.44
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.49
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.02
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.60
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.25
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.84
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.34
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.71
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.93
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.94
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.46
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.61
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.72
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.53
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.06
 p-value of test no 157                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.03
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.63
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.74
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.12
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.38
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.92
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.95
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.87
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.69
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.59
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5186.57
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.38
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.05
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.97
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.11
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.39
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.05
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.68
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.51
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.03
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.99
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9956
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.21
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.02
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.28
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.40
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.41
 p-value of test no 218                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.93
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.41
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.91
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.51
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.39
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11632.30
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.68
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000095404
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.95
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000069883
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 246                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:27.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195985434.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27867
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 35                 :    0.9968
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.85
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.54
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.45
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.11
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.69
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.36
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.84
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.60
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.14
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 64                 :  9.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.43
 p-value of test no 65                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.45
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.48
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.19
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908471
   j =  2                              :            45757
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908599
   j =  2                              :            45696
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.13
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.68
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.67
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.77
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.29
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.32
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.26
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.09
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.48
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.42
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.37
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.69
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.38
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.77
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.05
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.95
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.50
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.77
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.98
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.68
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.99
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.12
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.12
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.89
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.14
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.33
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.63
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.06
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.82
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.55
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.07
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.47
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.20
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.03
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.34
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.13
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.42
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-3
 p-value of test no 186                :    0.9982
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.09
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.08
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9738.09
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.40
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.29
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.40
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.43
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.63
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.77
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.82
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.28
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999962438
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.61
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999923333
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 238                :    0.51
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:11.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196935706.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27868
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 11                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7527
 p-value of test no 20                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.56
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.50
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.21
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.86
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.31
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.52
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.40
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.25
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.77
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.73
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7198.98
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.81
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.64
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.10
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.78
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.21
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908761
   j =  2                              :            45609
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908371
   j =  2                              :            45804
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.51
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.46
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.20
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.20
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.89
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.98
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.01
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.81
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.99
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.70
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.09
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.46
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.53
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.40
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.12
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.03
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.09
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.74
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.86
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.00
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.64
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.94
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.21
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  583.72
 p-value of test no 163                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.89
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.22
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.46
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.89
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.37
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.09
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.84
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.18
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.12
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.09
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.48
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.28
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.07
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.31
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.19
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.62
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.72
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.32
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.06
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.32e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.84
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.68
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.58
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3970.21
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.62
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.37
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.36
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999947273
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.21
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000002560
 
 Normal statistic for number of bits   :   0.020
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:29.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197918746.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27869
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.20
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.65
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.80
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.64
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  365.71
 p-value of test no 55                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.63
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.80
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.45
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.28
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.61
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.84
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.87
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908146
   j =  2                              :            45924
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908294
   j =  2                              :            45847
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.64
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.37
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.12
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.71
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.57
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.36
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.15
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.47
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.04
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.07
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17287.08
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.13
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.02
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.44
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.71
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.71
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.47
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.46
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.02
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.86
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.58
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.07
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.80
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.56
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.88
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.42
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.01
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.07
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.01
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.20
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.21
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.74
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.15
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.08
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.29
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.61
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.12
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.86
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.56
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.63
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.74
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.72
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.28
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.34
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.14
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.49
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.65
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.09
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.21
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.24
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.55
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.81
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.55
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999934352
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.40
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000031843
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    2.27
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:47.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198737946.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27870
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.97
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.81
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.55
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.04
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.43
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.91
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.12
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.44
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.22
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.02
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.19
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908717
   j =  2                              :            45637
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908566
   j =  2                              :            45708
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 74                 :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.91
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.15
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.97
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.91
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.79
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.73
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.54
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.13
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17749.17
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.10
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.21
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.26
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.60
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.21
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.56
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.07
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.12
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.91
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.47
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.28
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.06
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  213.54
 p-value of test no 161                :  2.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.89
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.07
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.86
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.65
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.94
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.21
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.43
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.03
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.92
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.62
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.03
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.48
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.78
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.92
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.47
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.52
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.48
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.15
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.46
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.73
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.16
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.40
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.19
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12132.90
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.66
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.94
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999920996
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.44
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999961313
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:38.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199720986.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27871
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 6                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 12                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5309
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7049
 p-value of test no 19                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.27
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.53
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.99
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.29
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.53
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.45
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  284.18
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.32
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.83
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.46
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.75
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.23
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.50
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.60
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.74
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908433
   j =  2                              :            45782
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907947
   j =  2                              :            46019
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 97                 :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.29
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.34
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.59
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.46
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.30
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.26
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.88
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.87
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.12
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.63
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.91
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.66
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.68
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.50
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.98
 p-value of test no 151                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.29
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.17
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.33
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.40
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.22
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.60
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.84
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.71
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.77
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.88
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.61
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.15
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.91
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.04
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.54
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.51
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.52
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.63
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.76
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.52
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5265.91
 p-value of test no 173                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.22
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.25
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.70
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.42
 p-value of test no 177                :    0.9922
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 180                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.00
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.08
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.12
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.96
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.86
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.11
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.63
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.91
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.66
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.19
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.85
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.58
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000010579
 
 Normal statistic for number of bits   :   0.084
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.94
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999927338
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:20.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  19  BirthdaySpacings, t = 8         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201064474.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27872
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.88
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.15
 p-value of test no 41                 :  8.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.66
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.49
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.24
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.90
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.35
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.15
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.65
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.81
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.53
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.22
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908140
   j =  2                              :            45927
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46118
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907770
   j =  2                              :            46106
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 81                 :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  3.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.36
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.19
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.60
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   11.25
 p-value of test no 125                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.33
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.03
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.86
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.88
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.80
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.61
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.27
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.36
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.47
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.99
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.74
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.63
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.42
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.69
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.06
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.17
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.50
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.12
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.92
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.13
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.11
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.96
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.57
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.27
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.33
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.09
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.20
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.27
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.00
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.28
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.35
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.92
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.13
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.95
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.80
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.16
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.33
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.63
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.37
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.06
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.92
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.24
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.06
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.62
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.50
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999914186
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.44
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000026446
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    2.38
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:25.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202244122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27873
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.06
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.64
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.02
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.09
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.64
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.41
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.65
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.65
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.07
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 58                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 60                 :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.61
 p-value of test no 61                 :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.47
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.12
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.45
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5240.13
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45473
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869473
   j =  1                              :        399909059
   j =  2                              :            45463
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908296
   j =  2                              :            45846
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.65
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.75
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.89
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.48
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.69
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.22
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.92
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.04
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.50
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.57
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.90
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.53
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.51
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.86
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.00
 p-value of test no 152                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.19
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.48
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.81
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.53
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.03
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.51
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.50
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.30
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.61
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.61
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.19
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.72
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.36
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.07
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.83
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.24
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.66
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.32
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4777.28
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.69
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.35
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.00
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.85
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.05
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.33
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.42
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.49
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4710.14
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.26
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.20
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.07
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.82
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.76
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.00
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000009310
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.26
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000074230
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:02.59
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203259930.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27874
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 9                  :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7557
 p-value of test no 15                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.40
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.04
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.55
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.22
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.37
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.12
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.91
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.83
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.25
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.93
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.89
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5125.67
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908290
   j =  2                              :            45849
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
 p-value of test no 100                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.50
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.89
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.48
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.96
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.39
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.09
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.09
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.48
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.23
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.66
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.99
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.43
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.01
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.47
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.23
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.62
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.17
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.82
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.94
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.33
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.72
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.23
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.53
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.34
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.98
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.95
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.89
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.54
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.42
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.26
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.05
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.28
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.18
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.09
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.03
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.49
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.08
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.88
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.10
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.66
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.40
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.28
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.96
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.89
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.11
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.33
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.14
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.09
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.71
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000056128
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.20
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000150019
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:27.47
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204177434.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27875
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.33
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.29
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.14
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.24
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.76
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.29
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.83
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.53
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.83
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.73
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.11
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.92
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.30
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.58
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908454
   j =  2                              :            45770
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907787
   j =  2                              :            46096
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 83                 :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.76
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.41
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.16
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.52
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.59
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.60
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.33
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.37
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.47
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17163.82
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.91
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.46
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.95
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.75
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.30
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.42
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.31
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.00
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.99
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.79
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.70
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.88
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.21
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.92
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.07
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.79
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.83
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.90
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.11
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.61
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.73
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.24
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.14
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.00
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.37
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.74
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.41
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.68
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.06
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.10
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.71
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.78
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.93
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.74
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.46
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.40
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12029.29
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.84
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000196516
 
 Normal statistic for number of bits   :    1.55
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.65
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000128782
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:11.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205193242.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27876
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4182
 p-value of test no 17                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 20                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.18
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.85
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.71
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.26
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.25
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.82
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.01
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.59
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.81
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.35
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.40
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.54
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.51
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45551
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869551
   j =  1                              :        399908899
   j =  2                              :            45549
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908222
   j =  2                              :            45886
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.62
 p-value of test no 116                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.40
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.08
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.41
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.54
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.61
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.86
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.68
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.43
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.92
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.62
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.04
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.61
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.82
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.28
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.50
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.24
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.06
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.88
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.95
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.43
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.89
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.60
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.92
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.43
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.66
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.30
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.62
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.00
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.28
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.76
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.21
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.94
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.67
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.32
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.32
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.32
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.28
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.39
 p-value of test no 177                :    0.9915
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.75
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.23
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.15
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.31
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.91
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.09
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.24
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.26
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.91
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.92
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.45
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.95
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.78
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.07
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000149854
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.13
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999983549
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:34.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206209050.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27877
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9925
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.37
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.85
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.23
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.47
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.00
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.54
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.21
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.39
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.32
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.67
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.29
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.07
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.33
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907844
   j =  2                              :            46072
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46209
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870209
   j =  1                              :        399907584
   j =  2                              :            46205
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.97
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.77
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.16
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.25
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.92
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.20
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.47
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.80
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.33
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.25
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.59
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.16
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.69
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.21
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.23
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.92
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.87
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.23
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.93
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.48
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.51
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.46
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.95
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.41
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.95
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.56
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.38
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.60
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.84
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.83
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.64
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.92
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5178.85
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.98
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.02
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.98
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.77
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.41
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.87
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.58
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.52
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 185                :  5.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 187                :  9.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.11
 p-value of test no 189                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.81
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 200                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.70
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.71
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.99
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.13
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.80
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.14
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.32
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.81
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.38
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.81
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.65
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999917177
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999810476
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    2.10
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:21.12
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207355930.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27878
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.18
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.43
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 45                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.10
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.21
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.94
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.26
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.99
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.99
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.72
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.18
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.51
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.10
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.51
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.40
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.77
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5299.75
 p-value of test no 68                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908062
   j =  2                              :            45966
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908211
   j =  2                              :            45893
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 85                 :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-3
 p-value of test no 87                 :    0.9984
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9912
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.49
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.56
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.73
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.04
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.98
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.26
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 128                :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.28
 p-value of test no 129                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.30
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.02
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 139                :    0.9911
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.28
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17663.20
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.93
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.28
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.30
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.04
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.09
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.84
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.18
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.83
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.16
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.67
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.37
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.47
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.07
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.89
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.35
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.46
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.35
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.19
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.59
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.35
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.20
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.03
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.94
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.58
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.28
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.90
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.10
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-4
 p-value of test no 194                :    0.9975
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.08
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.72
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.77
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.51
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9768.37
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.30
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.50
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.41
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.65
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.93
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.22
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.57
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999939266
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.37
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999988613
 
 Normal statistic for number of bits   :  -0.090
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208404506.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27879
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.36
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.01
 p-value of test no 49                 :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.73
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.69
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.25
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.76
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.78
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.61
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.46
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.46
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.13
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.11
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.39
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.64
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908140
   j =  2                              :            45924
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908585
   j =  2                              :            45706
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.81
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.42
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.59
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.17
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.22
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.10
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 127                :    0.9968
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.25
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.21
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.54
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.31
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.53
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.62
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.90
 p-value of test no 147                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.97
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.56
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.87
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.25
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.50
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.73
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.38
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.84
 p-value of test no 157                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.91
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.51
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.77
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.41
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.10
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.61
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.81
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.98
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.88
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.42
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.94
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.68
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.99
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.97
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.83
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.58
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.90
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.90
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.23
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.64
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.07
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.32
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.62
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.83
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.41
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9942
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.60
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.73
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.72
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.30
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11682.73
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.84
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999884474
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.50
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999979991
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    2.12
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:59.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209453082.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27880
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.52
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.64
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.81
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.96
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.21
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.55
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.76
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.60
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.79
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.29
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.18
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 64                 :    0.9976
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.67
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.07
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.91
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4867.05
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908432
   j =  2                              :            45772
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908197
   j =  2                              :            45894
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 106                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-5
 p-value of test no 109                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.62
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.11
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.59
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.88
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.01
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.25
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.78
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.17
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.71
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.16
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.48
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.93
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.36
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.88
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.69
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.52
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.54
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.83
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.69
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.26
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.12
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.33
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.30
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.49
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.66
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.25
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.84
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.02
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.25
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.96
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.88
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.76
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.80
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.33
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.90
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.06
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.36
 p-value of test no 179                :    0.9908
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.23
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.14
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.72
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.77
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.16
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.68
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.01
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.62
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.00
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.86
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.81
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.51
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.71
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999995951
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.24
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000025129
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 237                :    0.9952
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.034
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:37.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189595670.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27881
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5289
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.03
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.02
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.98
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.76
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.22
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.39
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.59
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.46
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.34
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.85
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.03
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.00
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.06
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   18.96
 p-value of test no 66                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.58
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.47
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908128
   j =  2                              :            45933
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908452
   j =  2                              :            45765
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.83
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.99
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.83
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.27
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.06
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.52
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.66
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.29
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.35
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.71
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.84
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.65
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.81
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.28
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.32
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.59
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.45
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.01
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.36
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.77
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.53
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.18
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.88
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.16
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.97
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.21
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.86
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.85
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.50
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.67
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.23
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.42
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.52
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.36
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.95
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.37
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.45
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.48
 p-value of test no 179                :  6.6e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 185                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.20
 p-value of test no 189                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.23
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.52
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.60
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.35
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.67
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.40
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.14
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.31
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.60
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.31
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.92
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.21
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000111775
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.64
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999907583
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:55.75
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190709782.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27882
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.91
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.59
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.15
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.44
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.35
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.20
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.94
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.75
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.09
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 64                 :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   36.48
 p-value of test no 65                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.67
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.44
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.37
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908286
   j =  2                              :            45851
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908431
   j =  2                              :            45780
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-5
 p-value of test no 79                 : 1 -  2.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.81
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.54
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.23
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.43
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.79
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.97
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.31
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.43
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.34
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.85
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17773.31
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.51
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.27
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.38
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.88
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.31
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.57
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.12
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.32
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.78
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.60
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.20
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.18
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.96
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.12
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.79
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.96
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.61
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.14
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.15
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.55
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.80
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.00
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.68
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.77
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.74
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.31
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.25
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.43
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9693.52
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.49
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.82
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.80
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.19
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.83
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.00
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12038.36
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.21
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999877169
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.01
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000006157
 
 Normal statistic for number of bits   :   0.049
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 243                :    0.9903
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:35.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191660054.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27883
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 4                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.62
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.74
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.55
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.92
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.61
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.56
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.75
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.76
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.34
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-3
 p-value of test no 58                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.94
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.81
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.63
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.06
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907859
   j =  2                              :            46063
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908544
   j =  2                              :            45725
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 86                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 101                :    0.9955
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 115                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.89
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.98
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.88
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.98
 p-value of test no 122                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.08
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.68
 p-value of test no 124                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.72
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 126                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.62
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.95
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.26
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.10
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.51
 p-value of test no 136                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 138                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.05
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.42
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.27
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.54
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.63
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.80
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.88
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.53
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.52
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.05
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.24
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.46
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.83
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.17
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.42
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.16
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.74
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.67
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.33
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.08
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.13
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  450.82
 p-value of test no 169                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.52
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.98
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.69
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4762.77
 p-value of test no 173                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.18
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.13
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.069
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 185                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.45
 p-value of test no 188                :    0.9928
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.08
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.41
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.52
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.39
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.03
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.25
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.03
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.14
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4353.86
 p-value of test no 227                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.18
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.86
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11491.13
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.54
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000004363
 
 Normal statistic for number of bits   :   0.034
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.22
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999911021
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.71
 p-value of test no 235                :  6.5e-6    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 236                :    0.9998    *****
 
 Anderson-Darling statistic = A2       :   11.79
 p-value of test no 237                :  2.2e-6    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -4.87
 p-value of test no 238                : 1 -  5.6e-7    *****
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:15:58.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0              1 -  5.6e-7
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192512022.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27884
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 3                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4535
 p-value of test no 16                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.79
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.08
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.64
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.33
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.62
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.86
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.71
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.36
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.53
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.07
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.70
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.28
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.16
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.20
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.16
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908113
   j =  2                              :            45942
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908684
   j =  2                              :            45652
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.80
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.36
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.51
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.94
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.34
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.24
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.26
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.60
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.09
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.66
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.32
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.72
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.69
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.26
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.67
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.33
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.35
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.52
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.63
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.74
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.12
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.54
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.95
 p-value of test no 159                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.86
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.38
 p-value of test no 161                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.19
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.97
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.88
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.00
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.66
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.30
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.44
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.24
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.79
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.93
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.70
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.21
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.84
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.10
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.03
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.60
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.55
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.51
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.12
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5074.63
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.90
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.08
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.68
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.59
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.68
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.77
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999939905
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.78
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000063259
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.64
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:05.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194052118.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27885
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.12
 p-value of test no 38                 :    0.9998    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.29
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.19
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.83
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.11
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.22
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.61
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.31
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.42
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.66
 p-value of test no 58                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.66
 p-value of test no 61                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.75
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.21
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.55
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.40
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908814
   j =  2                              :            45584
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45633
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869633
   j =  1                              :        399908736
   j =  2                              :            45629
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-4
 p-value of test no 110                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 111                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.55
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.17
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.94
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.79
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.89
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.89
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.82
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.53
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.15
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.67
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.52
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.93
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.02
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.19
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.97
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.39
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.12
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.89
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.02
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.06
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.84
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.83
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.48
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.01
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.29
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.28
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.07
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.77
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.74
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.95
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.15
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.04
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.12
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.64
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.36
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.67
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.52
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.70
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.04
 p-value of test no 176                :    0.9952
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.61
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.01
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.16
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.65
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.70
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.91
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.75
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.51
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.23
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.46
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.51
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.01
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.25
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999779195
 
 Normal statistic for number of bits   :   -1.75
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.43
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999961799
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 253                :    0.47
 
 Sample variance                       :    2.07
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:06.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195035158.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27886
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.93
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.89
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.85
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.03
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.83
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.12
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.58
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.28
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.96
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.80
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.14
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.42
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.70
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.99
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.78
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908171
   j =  2                              :            45910
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908557
   j =  2                              :            45720
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 114                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.65
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.86
 p-value of test no 120                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.21
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.83
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.00
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.26
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.50
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.07
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.95
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.80
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.83
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17248.20
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.64
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.04
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.14
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.97
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   39.33
 p-value of test no 150                :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.56
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.98
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.63
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.03
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.22
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.62
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.47
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.33
 p-value of test no 159                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.84
 p-value of test no 160                :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.48
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.83
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.51
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.72
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.25
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.75
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.69
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.91
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.61
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.53
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.67
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5217.57
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.32
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.10
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.14
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.44
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.50
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.16
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.41
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10274.78
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.59
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.86
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.27
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.70
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.49
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12154.60
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.92
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.50
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000100717
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.18
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000047191
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:08.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196018198.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27887
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    3.55
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.76
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.45
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.77
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.56
 p-value of test no 51                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.84
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.37
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.79
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.95
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.38
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.54
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.68
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.03
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.26
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.42
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.06
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908458
   j =  2                              :            45768
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908340
   j =  2                              :            45827
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 98                 :    0.9930
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.51
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.51
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.40
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.97
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.33
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.08
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.04
 p-value of test no 129                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.09
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.51
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17557.55
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.60
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.76
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.71
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.51
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.49
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.15
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.65
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.43
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.80
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.46
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.42
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.49
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.56
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.35
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.32
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.93
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.53
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.69
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.94
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.80
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.32
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.46
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.18
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.92
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.28
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.11
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.29
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.76
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.79
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.04
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4331.97
 p-value of test no 227                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3921.38
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.18
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.64
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.18
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999981275
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.49
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000130777
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:11.73
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197001238.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27888
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.52
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.48
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.17
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.18
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.16
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.53
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.06
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.81
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6935.46
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.08
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.96
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.64
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.94
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5175.87
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908596
   j =  2                              :            45696
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908035
   j =  2                              :            45981
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.78
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.03
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.40
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.06
 p-value of test no 122                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.86
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.42
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   53.21
 p-value of test no 125                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.66
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.87
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.83
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.53
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.73
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.77
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.03
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.58
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.82
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.70
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.63
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.86
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.26
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.06
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.54
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.83
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.88
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.60
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.24
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.64
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.59
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.71
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.35
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.40
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.44
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.00
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.63
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.52
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.79
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.66
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.66
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 201                :    0.9923
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.91
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.53
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.82
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.72
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5075.65
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.54
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.25
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.89
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.68
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.85
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.93
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999992300
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.16
 p-value of test no 233                :    0.9921
 
 
 -----------------------------------------------
 Total number of bits:  7999991220
 
 Normal statistic for number of bits   :  -0.069
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:57.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197853206.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27889
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.43
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.83
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.75
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.13
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.14
 p-value of test no 53                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.62
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.09
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.47
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.79
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.16
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.13
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.53
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.70
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.81
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907742
   j =  2                              :            46126
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907928
   j =  2                              :            46033
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.16
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.31
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.03
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.75
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.71
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.34
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.81
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.00
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.48
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.73
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17759.74
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.14
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.15
 p-value of test no 149                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.64
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.01
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.17
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.45
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.43
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.51
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.75
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.21
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.34
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.01
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.90
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.84
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.18
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.19
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.07
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.52
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.75
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.04
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.12
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.81
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.99
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.10
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.88
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.30
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.95
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.70
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.93
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.91
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.97
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.13
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.38
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.07
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.44
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.88
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.02
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.45
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.27
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.12
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.43
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.23
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000063199
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.82
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999935795
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.028
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:52.03
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199196694.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27890
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9919
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.18
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.30
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.04
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.41
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.05
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.37
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6801.42
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 60                 :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.97
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.91
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.47
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.64
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.77
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907937
   j =  2                              :            46030
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908400
   j =  2                              :            45794
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 72                 :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 74                 :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9914
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.54
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.23
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.42
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.49
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.25
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.72
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.86
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.28
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.06
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.55
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 142                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17713.88
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.74
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.85
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.97
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.44
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.90
 p-value of test no 150                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.44
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.35
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.70
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.94
 p-value of test no 157                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.54
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.79
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.02
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.72
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.25
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.40
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.50
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.58
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.55
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.41
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.02
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.96
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.29
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.13
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.89
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  456.89
 p-value of test no 174                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.23
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.43
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.63
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.66
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.03
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.62
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.41
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.80
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.12
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.26
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.76
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.87
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.73
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.03
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.52
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000043288
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000052009
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:41.94
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200179734.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27891
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1500
 p-value of test no 11                 :  1.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334620
   j =  1                              :        599997000
   j =  2                              :             1500
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7107
 p-value of test no 15                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.46
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.39
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.39
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.67
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.30
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.16
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.67
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.80
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.17
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.01
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.41
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.98
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5217.54
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908340
   j =  2                              :            45824
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907933
   j =  2                              :            46029
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-3
 p-value of test no 91                 :    0.9986
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.88
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.54
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.52
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.05
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.61
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.98
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.07
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.66
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.38
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.65
 p-value of test no 136                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.15
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.14
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.14
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.28
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.02
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.06
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.13
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.73
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.24
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.97
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.10
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.19
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.86
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.53
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.18
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.79
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.48
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.30
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.71
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.62
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.19
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.31
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.82
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.86
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.33
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.05
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.53
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.61
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.48
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.97
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.22
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-4
 p-value of test no 181                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.08
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.97
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.54
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.38
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.37
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.17
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.65
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.14
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.65
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.69
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.15
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.34
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999985103
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.91
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999979013
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:36.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           1.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201326614.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27892
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5596
 p-value of test no 13                 :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.59
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.29
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.31
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.93
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.36
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.46
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.52
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.85
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.41
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.43
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.91
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.97
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.15
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.06
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908994
   j =  2                              :            45500
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908619
   j =  2                              :            45683
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 87                 :  2.3e-3
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.14
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.22
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.45
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.13
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.57
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.71
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.94
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 128                :    0.9995    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.40
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.30
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   20.99
 p-value of test no 135                :  1.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.50
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17322.74
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.43
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.98
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.24
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.68
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.38
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.00
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.91
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.39
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.87
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.09
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.48
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.76
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.34
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.55
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.35
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.63
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.33
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.24
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.70
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.44
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.88
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.17
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.15
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.75
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.09
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.08
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.11
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.07
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.81
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.38
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.90
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.14
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.71
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.62
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.17
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.03
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.74
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.13
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.54
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.58
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.55
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.47
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999995000
 
 Normal statistic for number of bits   :  -0.040
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999923402
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 251                :    0.9919
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.13
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:30.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202375190.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27893
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 11                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9918
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.09
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.40
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.31
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.96
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.90
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.36
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.02
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.53
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.12
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.03
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.06
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.11
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.46
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.63
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908189
   j =  2                              :            45901
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908709
   j =  2                              :            45635
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.69
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.55
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.63
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.79
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.53
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.65
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.97
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.38
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.89
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.51
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17235.17
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.15
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.78
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.35
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.07
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.67
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.39
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.12
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.60
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.03
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.48
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.99
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.11
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.93
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.66
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.55
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.09
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.41
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.07
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.15
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.58
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.16
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.59
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.25
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.12
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.48
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.35
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.72
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.67
 p-value of test no 179                :    0.9962
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.21
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.72
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.73
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.24
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.73
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.64
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.65
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.99
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.42
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.41
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.73
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000060619
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999953030
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    2.46
 p-value of test no 249                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:58.77
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203292694.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27894
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.65
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.10
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.57
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.22
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.17
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.05
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.99
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.16
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.03
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.32
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.28
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.66
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.95
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.59
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908010
   j =  2                              :            45989
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908428
   j =  2                              :            45780
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.21
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  105.66
 p-value of test no 120                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.79
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.11
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.19
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.91
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.22
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17754.11
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.60
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.71
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.30
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.87
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.94
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.59
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.50
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.54
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.74
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.69
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.54
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.62
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.85
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.34
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.35
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.19
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.15
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.71
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.46
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.77
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.81
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.83
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.57
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.83
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.23
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.32
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.11
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.27
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.84
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.05
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.16
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.98
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.50
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.04
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10174.07
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.79
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.21
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.47
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.10
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.25
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.44
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.26
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.20
 p-value of test no 231                :  5.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000165355
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.07
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999773216
 
 Normal statistic for number of bits   :   -1.79
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:21.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204275734.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27895
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 4                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5315
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4502
 p-value of test no 14                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.25
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.99
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.18
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.70
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.55
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.84
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.49
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.74
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.97
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.06
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.96
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.10
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907739
   j =  2                              :            46123
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908339
   j =  2                              :            45823
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  9.8e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.41
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.38
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.68
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.24
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.94
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.78
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.82
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.11
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.31
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.82
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.55
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.61
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.48
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.61
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.31
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.35
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.24
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.12
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.15
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.23
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.59
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.01
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.61
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.82
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.58
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.09
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.45
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.79
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.44
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.63
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.36
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.68
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.93
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.33
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.03
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.06
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.08
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.93
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.19
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.41
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.39
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.08
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.03
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.57
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.36
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.79
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.17
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.91
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.45
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.00
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.40
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000048574
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.30
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000135946
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205324310.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27896
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.52
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.35
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   94.57
 p-value of test no 52                 :  5.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.40
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.77
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.54
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.60
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.05
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.78
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.82
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.07
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.15
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46368
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870368
   j =  1                              :        399907268
   j =  2                              :            46360
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908264
   j =  2                              :            45868
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 74                 :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 97                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
 p-value of test no 98                 :    0.9978
 
 Anderson-Darling statistic = A2       :    5.02
 p-value of test no 99                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.10
 p-value of test no 115                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.64
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.96
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.63
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.92
 p-value of test no 122                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.09
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.15
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.25
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.33
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.59
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.84
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.60
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.04
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.92
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.81
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.40
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.95
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.90
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.49
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.99
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.57
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.35
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.48
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.46
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.61
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.81
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.39
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.80
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.20
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.25
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.59
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.48
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.23
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.54
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.55
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.96
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.67
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.39
 p-value of test no 177                :  8.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.66
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.92
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.79
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.14
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.08
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.33
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.97
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.83
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.49
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.29
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.24
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.07
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.88
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000017929
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.12
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000136984
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:01.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         5.3e-4
  55  SampleCorr, k = 1               0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206340118.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27897
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     834
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.48
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    3.38
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.33
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.55
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.56
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.19
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.98
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.95
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.15
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.40
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.25
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.95
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.06
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.72
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.25
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.78
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907987
   j =  2                              :            46002
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-4
 p-value of test no 110                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    5.05
 p-value of test no 111                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.97
 p-value of test no 117                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.72
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.98
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.76
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.77
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.93
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.00
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.21
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.78
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.78
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.05
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.36
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.63
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.82
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.04
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.06
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.29
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.06
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.73
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.71
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.07
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.14
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.76
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.32
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.89
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.59
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.22
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.87
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.56
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.75
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.80
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.97
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.19
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.43
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.18
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.56
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.28
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.75
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.09
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.82
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.31
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.55
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.65
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10229.87
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.27
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.69
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.89
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.76
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.42
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.37
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.65
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999894305
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.34
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999992867
 
 Normal statistic for number of bits   :  -0.056
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    2.05
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:48.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207290390.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27898
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 12                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5533
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.20
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.42
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.66
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.16
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.52
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.93
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.69
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7205.99
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.54
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.40
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.98
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.16
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.04
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907895
   j =  2                              :            46045
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908139
   j =  2                              :            45926
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.33
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.67
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.88
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.04
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.37
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.17
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.83
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.97
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.81
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.77
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.19
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.52
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.41
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.29
 p-value of test no 150                :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.32
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.87
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.16
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.56
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.57
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.68
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.84
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.72
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.42
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.80
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.61
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.51
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.58
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.61
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.15
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.24
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.04
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.58
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4743.91
 p-value of test no 173                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.82
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.01
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.23
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.58
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.43
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.10
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.87
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.48
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9654.97
 p-value of test no 215                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5076.37
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4688.30
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.27
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.72
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.54
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.22
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.44
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999986507
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.78
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000018418
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.53
 p-value of test no 248                :  5.7e-3
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:47.60
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208338966.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27899
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5589
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.39
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.09
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.83
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.46
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.46
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.58
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.79
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.63
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.33
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.28
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.09
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.07
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.58
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.08
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.18
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46449
 p-value of test no 70                 :  4.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870449
   j =  1                              :        399907105
   j =  2                              :            46443
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908182
   j =  2                              :            45903
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.41
 p-value of test no 115                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.30
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.02
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.36
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.03
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.23
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.03
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.75
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.07
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.29
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.87
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.97
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.32
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.69
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.12
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.75
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.04
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.08
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.93
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.75
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.83
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.56
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.85
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  409.48
 p-value of test no 158                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.97
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.31
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.90
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.89
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.80
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.13
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.70
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.31
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.38
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.11
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.51
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.27
 p-value of test no 171                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.83
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.01
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.74
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.61
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.31
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.24
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.91
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.88
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.11
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10264.40
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.05
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.71
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.38
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.43
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.21
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.24
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.46
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000062038
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.89
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000014362
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.073
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 243                :    0.46
 
 Sample variance                       :    2.24
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:00:25.14
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209387542.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27900
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 5                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.11
 p-value of test no 42                 :    0.9999    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.14
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.93
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.52
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.02
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.55
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.80
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.68
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.58
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.63
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.14
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.77
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.65
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.15
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.59
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907936
   j =  2                              :            46026
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908433
   j =  2                              :            45779
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
 p-value of test no 80                 :    0.9984
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.77
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.34
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.07
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.56
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.32
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.31
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.08
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17267.26
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.17
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.61
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.81
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.11
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.59
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.27
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.17
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.80
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.61
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.37
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.34
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.05
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.49
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.53
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.19
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.52
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.01
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.34
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.01
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.66
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.41
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.35
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.45
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.53
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.93
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.11
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.95
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.46
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.81
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.79
 p-value of test no 178                :  4.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.05
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.83
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.25
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.66
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.11
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.65
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.95
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3889.54
 p-value of test no 228                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.39
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.63
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.49
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999939269
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999859793
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:18:04.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189628439.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27901
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.05
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.62
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.11
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.82
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.04
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.84
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.08
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.47
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.77
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.31
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.32
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.23
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.31
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.05
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908228
   j =  2                              :            45883
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908173
   j =  2                              :            45906
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.76
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.42
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.77
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.74
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.50
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.20
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.58
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.59
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.65
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.45
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.92
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.52
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.48
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.15
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.49
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.90
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.35
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.11
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.73
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.36
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.81
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.94
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.65
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.46
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.86
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.93
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.70
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.39
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.89
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.79
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.75
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.42
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.98
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.39
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.64
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.73
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.83
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.49
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.02
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.65
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.54
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.16
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.99
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.02
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.77
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 209                :    0.9953
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9609.03
 p-value of test no 211                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.11
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.87
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 223                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.65
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.80
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.68
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.60
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.25
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.44
 p-value of test no 231                :    0.9912
 
 
 -----------------------------------------------
 Total number of bits:  8000143689
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.03
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000242101
 
 Normal statistic for number of bits   :    1.91
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:41.53
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190578688.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27902
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 12                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.37
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.26
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.81
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.50
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.68
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.79
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.12
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.99
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.16
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.81
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.21
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 64                 :    0.9968
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.98
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.72
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.07
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.23
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908406
   j =  2                              :            45791
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45381
 p-value of test no 71                 :    0.9901
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869381
   j =  1                              :        399909239
   j =  2                              :            45379
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-3
 p-value of test no 86                 :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  9.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 102                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.78
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.69
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.59
 p-value of test no 122                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.46
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.42
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.77
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.78
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.82
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17106.95
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.60
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.04
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.07
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.18
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.15
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.30
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.66
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.13
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.83
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.32
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.81
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.42
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.76
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.75
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.13
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.60
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.82
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.21
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.87
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.30
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.17
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.68
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.40
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.74
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.96
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.17
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.07
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    2.17
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.64
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.29
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.87
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.11
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.99
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.37
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.71
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.22
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.78
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.22
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11445.71
 p-value of test no 229                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.71
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.60
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000052042
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.96
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000005818
 
 Normal statistic for number of bits   :   0.046
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 245                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 248                :  4.7e-3
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:14.76
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191594496.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27903
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 11                 :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.83
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.19
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.24
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.66
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.52
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.34
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.99
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.65
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.72
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.10
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.69
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.71
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5153.70
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908274
   j =  2                              :            45851
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908381
   j =  2                              :            45802
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.15
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.53
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.92
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.28
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.54
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.33
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.26
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.28
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.65
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.66
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.11
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.49
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.57
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.67
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.12
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.69
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.75
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.39
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.56
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.24
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.68
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.38
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.82
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.27
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.02
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.58
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.74
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.02
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.91
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.30
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.06
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.22
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.92
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.70
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.72
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.30
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.91
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 182                :    0.9990
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.03
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.45
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.85
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.01
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.47
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.44
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.40
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.34
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.44
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.49
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.24
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.64
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999963404
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.50
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999944150
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:41.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192544768.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27904
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.58
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.77
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.81
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.36
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.06
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.49
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.31
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.08
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.18
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.48
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.02
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.38
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.49
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908553
   j =  2                              :            45716
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907951
   j =  2                              :            46020
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 86                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 87                 :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 88                 :  5.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  2.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.62
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.74
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.02
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.10
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.50
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.74
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.27
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.76
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.74
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.63
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.32
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.94
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.24
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.23
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.02
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.35
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.43
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.12
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.80
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.68
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.05
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.06
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.65
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.63
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.69
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.83
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.70
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.50
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.12
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.45
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.67
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.66
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.50
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.14
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.37
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.31
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.97
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.75
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.08
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.55
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.66
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.20
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.68
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.18
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.98
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.64
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.97
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.97
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.76
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4324.17
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.13
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.88
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.94
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000003790
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.50
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000058237
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:21.61
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193331200.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27905
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    8.40
 p-value of test no 29                 :  8.0e-5    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.75
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.20
 p-value of test no 47                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.20
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.22
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.68
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.24
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.38
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.58
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.42
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.17
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.47
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.56
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.18
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5216.05
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46332
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870332
   j =  1                              :        399907339
   j =  2                              :            46326
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908556
   j =  2                              :            45722
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.96
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.43
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.46
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.59
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.10
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.89
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.17
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.39
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.06
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.99
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.41
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.76
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.11
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.98
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.88
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.40
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.11
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.73
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.82
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.15
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.31
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.42
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.80
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.39
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.43
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.40
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.13
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.63
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.00
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.08
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.25
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.76
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.76
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9937
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :1.40e-16
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.79
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.97
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.91
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.66
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.79
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.88
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.71
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.63
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.04
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.59
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11501.24
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.56
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999920456
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.68
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999884483
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:02.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP, t = 5           8.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194772992.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27906
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 4                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 10                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.63
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.12
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.70
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.82
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.03
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.38
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.74
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.78
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6772.72
 p-value of test no 57                 :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.95
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.59
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.36
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.12
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5280.46
 p-value of test no 68                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908743
   j =  2                              :            45621
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908631
   j =  2                              :            45680
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.98
 p-value of test no 116                :  3.4e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.51
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.71
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.02
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.55
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.48
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.23
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.40
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.85
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.82
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17795.97
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.74
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.06
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.48
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.07
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.35
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.82
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.11
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.80
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.05
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.93
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.16
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.17
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.07
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.94
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.73
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.69
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.03
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.97
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.14
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.42
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.66
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.68
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.88
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.94
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.47
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.89
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.33
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.44
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.81
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.65
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.17
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.91
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.07
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.24
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.66
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.67
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.86
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.14
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.63
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.49
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.87
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000136789
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.99
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999981512
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:59.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               3.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195624960.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27907
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.57
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.90
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.30
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.13
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.51
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.03
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.79
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.64
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.96
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.61
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.99
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908373
   j =  2                              :            45809
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908299
   j =  2                              :            45849
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.69
 p-value of test no 115                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.23
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.65
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.07
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.88
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.45
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.33
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.94
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.41
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17282.85
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.21
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.92
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.46
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.22
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.91
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.28
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.59
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.63
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.00
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.85
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.29
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.73
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.58
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.02
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.91
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.92
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.41
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.00
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.12
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.85
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.24
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.69
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.29
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.70
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.84
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.15
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  456.10
 p-value of test no 174                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.96
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.58
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.28
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.35
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.67
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.07
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.00
 p-value of test no 222                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.51
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.14
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.20
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.28
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.56
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.72
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000083452
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.51
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000048829
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    2.26
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:53.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196771840.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27908
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    5.09
 p-value of test no 38                 :  2.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 45                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.01
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.81
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.49
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.18
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.34
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.94
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.64
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.87
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.87
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.05
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.14
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.59
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.64
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.72
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908091
   j =  2                              :            45950
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908045
   j =  2                              :            45976
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.54
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.51
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.89
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.27
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.94
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.26
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.11
 p-value of test no 125                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.99
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.66
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.00
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
 p-value of test no 139                :    0.9980
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.52
 p-value of test no 141                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17700.17
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.48
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.11
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.54
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.27
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.24
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.18
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.50
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.87
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.07
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.82
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.94
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.99
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.13
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.14
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.07
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.70
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.78
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.62
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.46
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.02
 p-value of test no 165                :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.32
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.58
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.88
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.91
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.12
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.56
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.26
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.40
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.73
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.02
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.07
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.64
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.56
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.24
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.93
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.30
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.27
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.03
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.58
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.28
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.64
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.41
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.85
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999916085
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.07
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000015232
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:59.20
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197722112.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27909
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    3.44
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.50
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.03
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.68
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.88
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.28
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  501.24
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.20
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6834.91
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.26
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.89
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.94
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.16
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5221.08
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908334
   j =  2                              :            45827
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45288
 p-value of test no 71                 :    0.9971
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869288
   j =  1                              :        399909429
   j =  2                              :            45278
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-4
 p-value of test no 98                 :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.79
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.31
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.07
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.67
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.18
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.01
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.05
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.10
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.60
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.94
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.52
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.59
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.31
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.02
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.63
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.42
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.32
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.46
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.90
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.70
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.52
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.09
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.55
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.32
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.92
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.74
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.73
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.26
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.65
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.96
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.40
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.53
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.18
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.97
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.15
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.57
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.43
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.70
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.38
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.01
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.34
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.01
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.25
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.60
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.54
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.13
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12205.01
 p-value of test no 229                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.71
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.61
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000015661
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.45
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999957488
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:32.61
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198770688.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27910
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5603
 p-value of test no 13                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 45                 :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.23
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.59
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.02
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.39
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.76
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.64
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.18
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.03
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.61
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.56
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.06
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.29
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.67
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.34
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907737
   j =  2                              :            46127
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908395
   j =  2                              :            45795
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.90
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.20
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.24
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.81
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.90
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.21
 p-value of test no 124                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.64
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.50
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.20
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.16
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17155.59
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.95
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.71
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.06
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.58
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.73
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.34
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.32
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.45
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.49
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.79
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.27
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.10
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.71
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.24
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.77
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.08
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.07
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.27
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5214.47
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.16
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.57
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.53
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.45
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.39
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.56
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  144.11
 p-value of test no 175                :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.42
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.04
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.00
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.80
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.31
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.12
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 224                :    0.9912
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.87
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.28
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.75
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11535.48
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.81
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.20
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000027754
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.42
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999873779
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.56e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:32.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199753728.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27911
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5543
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9991    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.10
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.65
 p-value of test no 46                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.87
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.88
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.18
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.48
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.97
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.08
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.26
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.29
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.18
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.02
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.87
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.40
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46274
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870274
   j =  1                              :        399907455
   j =  2                              :            46268
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908569
   j =  2                              :            45711
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.47
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.89
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.12
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.86
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.57
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.36
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.54
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.03
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.25
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.25
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17749.34
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.82
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.37
 p-value of test no 147                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.19
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.90
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.01
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.09
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.17
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.82
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.90
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.79
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.92
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.61
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.19
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.81
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.12
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.69
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.88
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.91
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.11
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.19
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.79
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.74
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.39
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.89
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.72
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.33
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4812.55
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.89
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.94
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.79
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.14
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9780.68
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.42
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.67
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.76
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.64
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.40
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11484.89
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.42
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.43
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000148759
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.17
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000069520
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.13
 p-value of test no 239                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:02.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201195520.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27912
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.18
 p-value of test no 41                 :  7.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.06
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.57
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.86
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.19
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.22
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  292.35
 p-value of test no 54                 :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.77
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.64
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6826.75
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.64
 p-value of test no 59                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.16
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.70
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.35
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4794.25
 p-value of test no 68                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908224
   j =  2                              :            45885
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908506
   j =  2                              :            45741
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.96
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.32
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.75
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.65
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.48
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.03
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.47
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.28
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.58
 p-value of test no 134                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.14
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.56
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.41
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.92
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.15
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.77
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.93
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.27
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.32
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.06
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.78
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.03
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.59
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.07
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.58
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.99
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.88
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.91
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.97
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.77
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.62
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.37
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.42
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.70
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.03
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.39
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.89
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.67
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.72
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.78
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.90
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.70
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.69
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.64
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.93
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.66
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5025.39
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.00
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.28
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.90
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.04
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.71
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000047956
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.94
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000039571
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 246                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 247                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.68
 p-value of test no 248                :  3.7e-3
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 250                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:07.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202309632.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27913
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1490
 p-value of test no 11                 :  4.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334610
   j =  1                              :        599997020
   j =  2                              :             1490
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    3.40
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.01
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.94
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.92
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.59
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.08
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.10
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.65
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.42
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.55
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.66
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.23
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.11
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.71
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.32
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908489
   j =  2                              :            45754
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907692
   j =  2                              :            46148
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.27
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.61
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.98
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.24
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.51
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.52
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.78
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.15
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.27
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.75
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.20
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.32
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.88
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.64
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.05
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.52
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.75
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.79
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.85
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.58
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.91
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.87
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.12
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.65
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.94
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.16
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.71
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.63
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.48
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.14
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.67
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.33
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.21
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.53
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.25
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.03
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.25
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.09
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.41
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.54
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.72
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.75
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.34
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.11
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11623.66
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12213.27
 p-value of test no 230                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.11
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000174574
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999837791
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.086
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:53.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203489280.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27914
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4192
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    2.95
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.16
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.71
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.55
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.48
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.24
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.23
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.34
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.94
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.38
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.47
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.28
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.97
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.59
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5288.10
 p-value of test no 68                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908344
   j =  2                              :            45819
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908406
   j =  2                              :            45794
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 103                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 105                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 107                :    0.9936
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.74
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.76
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.99
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.70
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.11
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.69
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.92
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.69
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.24
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.11
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 142                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17157.12
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.03
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.88
 p-value of test no 147                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.82
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.76
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.60
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.33
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.83
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.23
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.94
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.71
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.82
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.62
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.88
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.45
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.59
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.85
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.45
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.19
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.61
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.98
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.14
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.54
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.80
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.07
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.59
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.76
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.50
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.86
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.84
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9751.74
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.69
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.98
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.38
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.26
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.85
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.10
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.08
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.24
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999964088
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.82
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999918134
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    2.03
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:38.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204505088.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27915
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 6                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4482
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.84
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.20
 p-value of test no 48                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.58
 p-value of test no 49                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.76
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.88
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.89
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.85
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.49
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.66
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.37
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.52
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.78
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.49
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.61
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907902
   j =  2                              :            46046
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907695
   j =  2                              :            46145
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.12
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.03
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.17
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.72
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.62
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.22
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.59
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.61
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.48
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.00
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17431.82
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.85
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.78
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.58
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.68
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.63
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.73
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.25
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.92
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.82
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.27
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.22
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  208.55
 p-value of test no 159                :  6.3e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.08
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.69
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.91
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.22
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.34
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.66
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.53
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.39
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.52
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.98
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.08
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.36
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  299.34
 p-value of test no 172                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.12
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  450.94
 p-value of test no 174                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.76
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.68
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.56
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.38
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.01
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.16
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.25
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.67
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.92
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.59
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.42
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.41
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12177.07
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.31
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.56
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999996809
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.09
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000083500
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:55.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     6.3e-5
  79  RandomWalk1 M (L=10000, r=15)   0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205488128.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27916
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.06
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.97
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.51
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.52
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.31
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.88
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.17
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.49
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.82
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.78
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.79
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.28
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.23
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.70
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.18
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908132
   j =  2                              :            45928
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908198
   j =  2                              :            45892
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.67
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.90
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.41
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.74
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.52
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.21
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.43
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.89
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.77
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17449.50
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.33
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.71
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.96
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.68
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.23
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.00
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.86
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.81
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.42
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.63
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.10
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.40
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.05
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.12
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.77
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.78
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.59
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.93
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.07
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.00
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.10
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.61
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.13
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.81
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.36
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.78
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.45
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.02
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.74
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.73
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.86
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.88
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.61
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.28
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.45
 p-value of test no 217                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.34
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.14
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.79
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.00
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.84
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11550.55
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.37
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999923090
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.74
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999939215
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 235                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.82
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206471168.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27917
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.52
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.12
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.47
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.38
 p-value of test no 51                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.54
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.70
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.92
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.97
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.18
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.04
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.52
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.35
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.16
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.66
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908449
   j =  2                              :            45768
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907909
   j =  2                              :            46041
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.26
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.25
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.38
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.92
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.46
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.23
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.82
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 143                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 144                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17975.74
 p-value of test no 145                :  1.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.69
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.93
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.67
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.34
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.71
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.21
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.54
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.34
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.92
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.38
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.80
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.49
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.61
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.51
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.20
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.92
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.80
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.13
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.56
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4763.58
 p-value of test no 168                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.19
 p-value of test no 169                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.38
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.72
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.98
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.98
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.94
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.91
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.26
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.88
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 181                :    0.9918
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 183                :    0.9936
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.29
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.49
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
 p-value of test no 204                : 1 -  9.8e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 206                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  272.20
 p-value of test no 207                :  5.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.29
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.69
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.48
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.74
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.42
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.08
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.47
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11634.43
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.12
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999966176
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.33
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999990467
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:49.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207454208.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27918
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1246
 p-value of test no 5                  :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334366
   j =  1                              :        599997508
   j =  2                              :             1246
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.15
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.05
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.04
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.79
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.93
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.79
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7230.04
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-3
 p-value of test no 59                 :    0.9969
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.46
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.22
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.01
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.31
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908558
   j =  2                              :            45715
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907967
   j =  2                              :            46006
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 80                 :    0.9915
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.62
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.62
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.70
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.11
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.30
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.33
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.76
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.92
 p-value of test no 133                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.79
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.23
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.27
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.16
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.12
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.45
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.91
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.61
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.23
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.02
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.84
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.33
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.43
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.81
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.91
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.14
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.51
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.69
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.89
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.07
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.40
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.05
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.08
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  445.11
 p-value of test no 169                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.64
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.78
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.65
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.42
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.36
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.55
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.43
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.22
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.64
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.29
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.17
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.21
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 223                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.63
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.14
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.80
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.74
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.23
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.84
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000159181
 
 Normal statistic for number of bits   :    1.26
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000015214
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:46.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208437248.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27919
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5328
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.84
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.52
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.72
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.77
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.86
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  283.43
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.21
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.32
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.48
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.49
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.68
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.31
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.89
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.60
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907764
   j =  2                              :            46115
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908068
   j =  2                              :            45960
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.16
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.19
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.71
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.16
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.75
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.96
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.73
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.74
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.00
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17166.36
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.41
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.58
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.78
 p-value of test no 149                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.42
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.64
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.16
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.42
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.77
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.35
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.53
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.63
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.10
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.04
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.09
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.40
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.84
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.25
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.63
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.22
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.39
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.29
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.02
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.93
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.98
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.19
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.09
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.89
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.34
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.91
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.60
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.22
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.54
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.49
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.77
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.78
 p-value of test no 217                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.74
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.08
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.17
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.34
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11606.22
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.32
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999955223
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.50
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999983408
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   02:59:46.63
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209518592.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27920
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    5.43
 p-value of test no 26                 :  1.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    3.18
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.49
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.53
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.09
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.28
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.23
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.19
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.23
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1538.97
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.89
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.39
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 62                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.66
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.90
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.64
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.06
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907911
   j =  2                              :            46034
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907915
   j =  2                              :            46038
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.68
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.12
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.42
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.38
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.10
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.87
 p-value of test no 124                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.51
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.04
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.59
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.31
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.68
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.32
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.26
 p-value of test no 148                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.79
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.08
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.13
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.88
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.53
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.09
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.64
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.28
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.21
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.87
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.85
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.51
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.89
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.74
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.52
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.94
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.48
 p-value of test no 167                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.22
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.85
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.45
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.23
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.58
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.27
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.52
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.13
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.57
 p-value of test no 196                :    0.9915
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.20
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.18
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.17
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.27
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.69
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.48
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.91
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.30
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.86
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12112.92
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.15
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000126511
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.97
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000050026
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:16:36.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189661208.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27921
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5288
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.17
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.71
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.63
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.26
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.35
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.46
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.53
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.90
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.42
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.33
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.92
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.77
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907821
   j =  2                              :            46085
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908296
   j =  2                              :            45846
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.25
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.38
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.45
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.23
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.32
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.33
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.62
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.00
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.69
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.08
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.69
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.45
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.66
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.83
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.83
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.97
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.83
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.62
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.73
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.87
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.74
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.91
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.12
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.08
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.30
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.48
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.03
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.35
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.68
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.03
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4792.83
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.61
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.97
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.03
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.36
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.51
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.56
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.87
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.83
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.27
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.26
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.46
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.85
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.88
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.83
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.19
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.35
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.55
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11526.28
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.83
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.71
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000126343
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.64
 p-value of test no 233                :  8.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000032500
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
 p-value of test no 240                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.52
 p-value of test no 243                :  5.8e-3
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:18.13
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189956120.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27922
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 22                 :    0.9980
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.60
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.12
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.68
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.80
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.31
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.16
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.88
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.86
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.79
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.50
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.76
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.44
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.54
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.20
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908463
   j =  2                              :            45764
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908037
   j =  2                              :            45977
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.95
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.56
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.08
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.24
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.69
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.94
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.74
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.92
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.80
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.72
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.52
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.10
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.06
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.78
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.87
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.85
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.41
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.66
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.80
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.24
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.69
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.37
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.85
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.80
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.95
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.63
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.77
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.08
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.33
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.62
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.89
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.60
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.53
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.27
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.12
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.16
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.66
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.45
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.36
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.74
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.58
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.21
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.41
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.44
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.75
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.06
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.20
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.73
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.05
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.75
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.38
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999897590
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.81
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999857663
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:32.07
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191004696.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27923
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5257
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.37
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.36
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.96
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.98
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.18
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.39
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.82
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.27
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.20
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.61
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.20
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.01
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.23
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.80
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908219
   j =  2                              :            45889
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907664
   j =  2                              :            46159
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.84
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.32
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.43
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.49
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.39
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.70
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.42
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.41
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.11
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.62
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.90
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.24
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.75
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.53
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.29
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.47
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.52
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.86
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.49
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.00
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.25
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.67
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.09
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.83
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.36
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.11
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.20
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.08
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.78
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.21
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.59
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.35
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.15
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.10
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.95
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.35
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.90
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 181                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.18
 p-value of test no 184                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.22
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.16
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.92
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.31
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.11
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.89
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.39
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.05
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.30
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.26
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.93
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.89
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999925304
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.66
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000081799
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.019
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:42.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192086040.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27924
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9953
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    5.99
 p-value of test no 30                 :  9.9e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     675
 p-value of test no 31                 :  1.4e-3
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.46
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.48
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.94
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.71
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.46
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.31
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.89
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.43
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.49
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.64
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.56
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.63
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.16
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.59
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.48
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907898
   j =  2                              :            46051
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907883
   j =  2                              :            46045
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.77
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.60
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.55
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.04
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.34
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.44
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.71
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.94
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.42
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.58
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.66
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.20
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.36
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.06
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.26
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.61
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.55
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.81
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.07
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.09
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.74
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.63
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.00
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.65
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.83
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.20
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.00
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.02
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.00
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.06
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.56
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.58
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.95
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.48
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.97
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.72
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.49
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.18
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.30
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.68
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.62
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.16
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.72
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.12
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.80
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.36
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.37
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.06
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.50
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.26
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.02
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.85
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999834353
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.35
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000061747
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:30.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193101848.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27925
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.41
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.33
 p-value of test no 29                 :  6.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.30
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.55
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.38
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.38
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.09
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.32
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.20
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.27
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.01
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.49
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.13
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.31
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4938.66
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908508
   j =  2                              :            45740
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908760
   j =  2                              :            45608
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.67
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.44
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.47
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.27
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.97
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.81
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.37
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.59
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.05
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 142                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
 p-value of test no 143                :    0.9970
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 144                :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16966.11
 p-value of test no 145                :    0.9938
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.72
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.07
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.92
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.04
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.41
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.50
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.25
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.69
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.82
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.92
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.08
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.99
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.71
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.25
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.51
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.80
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.14
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.39
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.44
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.90
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.19
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.55
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.52
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.37
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.75
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.42
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.96
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.17
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.44
 p-value of test no 183                :  7.3e-3
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.29
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.05
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.17
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.92
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.78
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.87
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.43
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.16
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.34
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.33
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.95
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.85
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999920954
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.00
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999964850
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:17.25
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194150424.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27926
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.12
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.75
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.20
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.04
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.79
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.79
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.33
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.94
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.04
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.79
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.07
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.76
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.72
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907539
   j =  2                              :            46226
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908770
   j =  2                              :            45612
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.50
 p-value of test no 119                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.03
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.95
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.04
 p-value of test no 124                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.92
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.22
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.00
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.37
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17654.07
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.55
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.86
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.87
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.52
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.24
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.21
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.29
 p-value of test no 155                :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.99
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.81
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.15
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.88
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.68
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.55
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.59
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.11
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.35
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.43
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.39
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.42
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.42
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.47
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.32
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.11
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.96
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.41
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.19
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  1.0e-2
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.88
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.56
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.15
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.63
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.80
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.06
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.66
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.65
 p-value of test no 216                :  1.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.89
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.41
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.22
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4244.96
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.31
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11430.36
 p-value of test no 230                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.34
 p-value of test no 231                :  9.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999950804
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.01
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999951431
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.97
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 246                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 247                :  6.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.05
 p-value of test no 248                :    0.9988
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:15.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  92  HammingCorr, L = 30             1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195166232.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27927
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 3                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 11                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9907
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.73
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.19
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.25
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.47
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.66
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.22
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.19
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1284.13
 p-value of test no 56                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.07
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.85
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.57
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.67
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.41
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.42
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908048
   j =  2                              :            45973
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908120
   j =  2                              :            45937
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 95                 :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.04
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.81
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.14
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.28
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.60
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.16
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.62
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.35
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.58
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17613.46
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.52
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.52
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.00
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.46
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.48
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.27
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.08
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.76
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.41
 p-value of test no 157                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.39
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.30
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.02
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.37
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.61
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.60
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.23
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.13
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.62
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.18
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.25
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.45
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.68
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.81
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.84
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.90
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.37
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.44
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.97
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.80
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.33
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.10
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.23
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.26
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.92
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.62
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.94
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.50
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.46
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.93
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.10
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000016876
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.57
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999870260
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:05.36
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196247576.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27928
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.03
 p-value of test no 40                 :  9.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9904
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.85
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.65
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.76
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.90
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.74
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.23
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.79
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.40
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6945.74
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.69
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.88
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.86
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.56
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907682
   j =  2                              :            46150
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908111
   j =  2                              :            45937
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 118                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.85
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.77
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.96
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.92
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.62
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.37
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.33
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.34
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.37
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.23
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.18
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.34
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.54
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.27
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.11
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.32
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.16
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.48
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.33
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.45
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.61
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.85
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.15
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.36
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.29
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.70
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.08
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.82
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.03
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.28
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.69
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5183.35
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.01
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.19
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.70
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.67
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.88
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.51
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.83
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.90
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.60
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.25
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.11
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.67
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.28
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.28
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5134.89
 p-value of test no 226                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.21
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.04
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.65
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.54
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.88
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999978143
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999915056
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.20
 p-value of test no 254                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:05.10
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197459992.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27929
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.51
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.36
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.90
 p-value of test no 47                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.69
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.78
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.75
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.13
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.46
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.04
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.19
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.43
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.89
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.65
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.64
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.04
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.70
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.80
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908318
   j =  2                              :            45838
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907875
   j =  2                              :            46049
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.06
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.76
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.12
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.22
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.65
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.50
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.01
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.03
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.64
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.11
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 144                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.84
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.60
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.59
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.28
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.56
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.79
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.69
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.22
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.42
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.68
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.33
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.49
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.54
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.08
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.27
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.57
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.59
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.90
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.52
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.55
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.55
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.41
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.59
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.60
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.82
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.11
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.28
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.62
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.73
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.75
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.10
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.32
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.13
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 214                :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.65
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.77
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.52
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.65
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3897.56
 p-value of test no 228                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.80
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.39
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.80
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999948176
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.85
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999993809
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:23.84
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198475800.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27930
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 11                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4177
 p-value of test no 16                 :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.35
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.68
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.15
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.14
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.44
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.74
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.27
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.38
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.87
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.20
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.50
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.38
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.37
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.83
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4807.08
 p-value of test no 68                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46389
 p-value of test no 70                 :  8.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870389
   j =  1                              :        399907229
   j =  2                              :            46375
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908418
   j =  2                              :            45788
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.30
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.76
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.99
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.43
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.82
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.00
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17133.15
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.82
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.73
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.44
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.46
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.96
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.77
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.81
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.04
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.52
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.55
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.33
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.34
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.00
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.44
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.06
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.88
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.85
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.58
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.21
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.86
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.21
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.75
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.37
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.01
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.57
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.96
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.11
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.51
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.25
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.37
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.53
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.22
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.21
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.50
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12125.64
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.12
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.28
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999927002
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.25
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000051103
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:34.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199458840.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27931
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7555
 p-value of test no 21                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.27
 p-value of test no 40                 :  7.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.43
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.32
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.62
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.79
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.80
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.56
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.15
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.78
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.23
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.60
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.33
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.53
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.13
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.47
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.11
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.72
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45570
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869570
   j =  1                              :        399908863
   j =  2                              :            45564
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907989
   j =  2                              :            46001
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 94                 :    0.9939
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.00
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.40
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.32
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.77
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.34
 p-value of test no 123                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.10
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.99
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.07
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.13
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.35
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.47
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17577.72
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.15
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.85
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.33
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.31
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.08
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.23
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.81
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.37
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.14
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.77
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.41
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.64
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.15
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.01
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.70
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.28
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.09
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.77
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.10
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.66
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.92
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.23
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.02
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.47
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.00
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.23
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.33
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.83
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.32
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.75
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.09
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.88
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.15
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.74
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-4
 p-value of test no 219                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5137.07
 p-value of test no 222                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.79
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.45
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.12
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.27
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.34
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.85
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999850082
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.44
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999973652
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:03.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200605720.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27932
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 10                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.60
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.55
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    3.54
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.92
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.32
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.29
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.22
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.30
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.93
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.91
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.00
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.77
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.30
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.11
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.86
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.79
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4749.73
 p-value of test no 68                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908271
   j =  2                              :            45857
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907775
   j =  2                              :            46111
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.78e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.37
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.36
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.98
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.13
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.27
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.95
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.11
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.47
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.70
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.11
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.19
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.31
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.63
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.03
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   38.56
 p-value of test no 150                :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.47
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.61
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.89
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.35
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.47
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.20
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.27
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.47
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.75
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.24
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.17
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.02
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.77
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.08
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.88
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.94
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.26
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.72
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.29
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.81
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.33
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.88
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.96
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.96
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.73
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.55
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.54
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.36
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.62
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.55
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.20
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.61
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.91
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.43
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.13
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.98
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.74
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999752537
 
 Normal statistic for number of bits   :   -1.96
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.86
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000013870
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:36.00
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201588760.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27933
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     836
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.84
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.03
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.11
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.91
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.49
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.34
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.63
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.43
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.74
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.87
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.06
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.97
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.36
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.87
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.90
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45505
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869505
   j =  1                              :        399908992
   j =  2                              :            45501
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908267
   j =  2                              :            45862
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.03
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.86
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.08
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.47
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.27
 p-value of test no 123                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.47
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.69
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.78
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.64
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.86
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.79
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.56
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.51
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.26
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.08
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.06
 p-value of test no 150                :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.44
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.01
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.89
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.58
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.83
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.95
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.29
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.26
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.96
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.77
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.96
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.31
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.85
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.64
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.94
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.52
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.88
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.18
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.01
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.89
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.45
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.26
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.18
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.28
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.00
 p-value of test no 176                :  5.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.46
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.88
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.90
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.43
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.51
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.20
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.75
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.32
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.13
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12107.45
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.79
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999795098
 
 Normal statistic for number of bits   :   -1.62
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.98
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000055612
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:10.81
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202604568.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27934
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 5                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.57
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.48
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.16
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.46
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.36
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.80
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.56
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.44
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.19
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.25
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.42
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.84
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.30
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  163.56
 p-value of test no 67                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.07
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908387
   j =  2                              :            45802
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908128
   j =  2                              :            45933
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.23
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.72
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.88
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.22
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.33
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.91
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.27
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.00
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.34
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17749.36
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.54
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.24
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.91
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.41
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.66
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.41
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.18
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.62
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.69
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.44
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.19
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.91
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.24
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.83
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.72
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.40
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.14
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.69
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.30
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.06
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.95
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.02
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.61
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.19
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.72
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.72
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.48
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.21
 p-value of test no 178                :  7.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.66
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.64
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.30
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.01
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.27
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.87
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.31
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.43
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.01
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12042.71
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.49
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.32
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000070258
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.43
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999861629
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.91
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:42.70
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203653144.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27935
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 10                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    4.05
 p-value of test no 44                 :  8.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 45                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.13
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.09
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.82
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.22
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.82
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.51
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.53
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.75
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.25
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.33
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.63
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.94
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.89
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908740
   j =  2                              :            45627
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46243
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870243
   j =  1                              :        399907519
   j =  2                              :            46233
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.52
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.76
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.25
 p-value of test no 122                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.15
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.35
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.73
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.43
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.19
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.45
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.14
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.47
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.56
 p-value of test no 149                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.79
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.24
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.13
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.99
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.72
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.94
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.17
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.13
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.41
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.66
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.03
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.62
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.74
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.73
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.62
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.77
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5250.65
 p-value of test no 168                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.90
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.01
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.31
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.41
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.83
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.79
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.97
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.29
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.85
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.53
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9698.67
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.57
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.43
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.74
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.63
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.77
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.59
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.38
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.54
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000078169
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.53
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000071698
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:04.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204800024.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27936
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5616
 p-value of test no 13                 :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7537
 p-value of test no 20                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.50
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9960
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.28
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.66
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.51
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.62
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.62
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.64
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.64
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.78
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.15
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.40
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.29
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.33
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.93
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.53
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.57
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.98
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46190
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870190
   j =  1                              :        399907624
   j =  2                              :            46182
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46036
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907932
   j =  2                              :            46028
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.24
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.88
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.34
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.89
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.46
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.35
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.23
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.86
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.64
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.13
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.85
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.22
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.82
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.00
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.08
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.17
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.94
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.44
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.33
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.28
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.22
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.30
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.54
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.86
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.15
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.45
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.69
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.17
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.47
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.19
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.14
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.71
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.50
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.72
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.25
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.69
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.01
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.74
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.12
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.77
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.09
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9770.83
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.73
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.90
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.02
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.19
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.69
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.06
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.75
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000092923
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.08
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000069544
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:32.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205848600.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27937
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.69
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.09
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.75
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.52
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.92
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.89
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.72
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.19
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1546.51
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.94
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.76
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.09
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.60
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.63
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.58
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908552
   j =  2                              :            45715
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907985
   j =  2                              :            46003
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 88                 :    0.9996    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.83
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.38
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.48
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.47
 p-value of test no 122                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.71
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.15
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.46
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.34
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.34
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.44
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.61
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.96
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.30
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.00
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.20
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.23
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.65
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.98
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.16
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.46
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.88
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.48
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.75
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.79
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.33
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.49
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.48
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.63
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.47
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.82
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.25
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.10
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.79
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.49
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.63
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.19
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.18
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.92
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.39
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.33
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.01
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.52
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.08
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9711.92
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.35
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.93
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.96
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.25
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.52
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.04
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.70
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.11
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000201292
 
 Normal statistic for number of bits   :    1.59
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.75
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999941309
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 237                :  8.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.70
 p-value of test no 238                :    0.9965
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:56.44
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206831640.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27938
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7515
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.27
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.85
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.15
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.99
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.59
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.62
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.05
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7239.08
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.77
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.75
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.43
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.11
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.79
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908112
   j =  2                              :            45938
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907984
   j =  2                              :            46005
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.06
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.69
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.87
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.65
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.84
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.14
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.14
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.79
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.91
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17715.44
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.63
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.43
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.94
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.03
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.00
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.25
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.86
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.46
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.70
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.25
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.06
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.36
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.00
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.93
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.72
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.92
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.12
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.30
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.94
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.40
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.80
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.55
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.39
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.47
 p-value of test no 176                :  6.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.49
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.66
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.32
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.18
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.10
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.25
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9688.72
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.68
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 221                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.50
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.25
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.81
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.57
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.40
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.92
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.81
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999966761
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.37
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999877610
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:09.73
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207847448.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27939
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 9                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    4.36
 p-value of test no 26                 :  5.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.07
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.37
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   95.45
 p-value of test no 51                 :  4.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.50
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.38
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.45
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.31
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.52
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7223.74
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.21
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.35
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.29
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.49
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.78
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908585
   j =  2                              :            45703
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908044
   j =  2                              :            45972
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.90
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.01
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.78
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.76
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.85
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.74
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.56
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.45
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.01
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.16
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 139                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.10
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.36
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.62
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.33
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.66
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.16
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.99
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.40
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.05
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.39
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.04
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.48
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.72
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.27
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.29
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.88
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.07
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.75
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.31
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.78
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.02
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.93
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.92
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.93
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.91
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.79
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.59
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.47
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.05
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.29
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.27
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.92
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.14
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.35
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.77
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9732.05
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.42
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.70
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.58
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.05
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.17
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.88
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.59
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999835535
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.48
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000035725
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.28
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.19
 p-value of test no 249                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:52.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         4.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208896024.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27940
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    3.48
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.18
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.18
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.49
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.55
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.67
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.67
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.73
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1551.44
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.40
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.50
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.29
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.30
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.06
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908709
   j =  2                              :            45641
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908240
   j =  2                              :            45874
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.43
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.26
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.92
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.16
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.89
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.33
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.42
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.00
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.50
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.52
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.04
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.90
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.11
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.03
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.51
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.49
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.67
 p-value of test no 150                :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.52
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.79
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.38
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.04
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.44
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.64
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.63
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.89
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.30
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.68
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.59
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.70
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.87
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.42
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.67
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.74
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.27
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.32
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.07
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.40
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.85
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.10
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.27
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.94
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 187                :    0.9970
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.82
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.03
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.33
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.19
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.15
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.65
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.52
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.07
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.85
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.96
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.45
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.47
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999996803
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.79
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000103912
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-3
 p-value of test no 241                :    0.9977
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:21:06.11
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189693977.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27941
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.05
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.77
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.22
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.71
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.27
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.85
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.35
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.13
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.44
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.75
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 62                 :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.69
 p-value of test no 65                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.97
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.89
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4908.68
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46173
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907660
   j =  2                              :            46161
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908274
   j =  2                              :            45863
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.10
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.92
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.94
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.34
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.13
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.86
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.89
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.35
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.96
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17219.65
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.15
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.75
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.67
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.42
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.81
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.20
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.45
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.53
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.07
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.93
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.78
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.68
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.86
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.91
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.10
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.27
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.91
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.76
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.44
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.63
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.91
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.16
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.37
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.24
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.73
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.15
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.36
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.75
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.64
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.36
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.91
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.69
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.87
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.12
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.54
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.59
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.35
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.90
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.87
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 223                :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 225                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4636.77
 p-value of test no 226                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.58
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.38
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.37
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.52
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.61
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000012436
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.97
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000049573
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:53.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190775321.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27942
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.42
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.65
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    4.84
 p-value of test no 33                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.77
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.31
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.67
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.40
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.41
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.42
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.68
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.94
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.14
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.93
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.12
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.91
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.63
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.22
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.83
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907959
   j =  2                              :            46016
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907836
   j =  2                              :            46073
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 102                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 108                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-4
 p-value of test no 112                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.12
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.55
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.05
 p-value of test no 121                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.65
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.34
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.14
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.91
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.86
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.52
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.97
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.91
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.83
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.36
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.66
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.88
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.57
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.42
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.57
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.84
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.79
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.45
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.70
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.56
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.14
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.41
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.90
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.41
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.05
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.49
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.59
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.57
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.16
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.68
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.53
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.22
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.50
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.21
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.05
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.10
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.36
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.06
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 181                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.70
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.29
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.75
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.13
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.94
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.72
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.32
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.34
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.79
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.89
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.71
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.23
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.31
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000062809
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.39
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999957680
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:14:35.62
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191725593.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27943
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 6                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.59
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.88
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.35
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.04
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.44
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.18
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.64
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.75
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.45
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.00
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.74
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.69
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.60
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.98
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.84
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908134
   j =  2                              :            45930
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-6
 p-value of test no 109                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.94
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.25
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.14
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.06
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.85
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.84
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.60
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.074
 p-value of test no 135                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.54
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 142                :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 143                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 144                :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17958.56
 p-value of test no 145                :  2.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.82
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.82
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.54
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.43
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.81
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.48
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.77
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.11
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.90
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.52
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.90
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.70
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.43
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.79
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.37
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.53
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.14
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.51
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.82
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.33
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.73
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.13
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.44
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.28
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.17
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.15
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.10
 p-value of test no 179                :  9.8e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.36
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.42
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.26
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.65
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
 p-value of test no 208                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10378.25
 p-value of test no 211                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.78
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.19
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.39
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.79
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.80
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.67
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.23
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.11
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999997535
 
 Normal statistic for number of bits   :  -0.019
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.31
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000111193
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:44.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 29              9.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192610329.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27944
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.17
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9925
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.75
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.05
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.13
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.02
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.19
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.01
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.06
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.78
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.11
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.72
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.47
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.76
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.24
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.39
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907935
   j =  2                              :            46028
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908446
   j =  2                              :            45774
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.92
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.96
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.89
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.95
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.35
 p-value of test no 124                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.41
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.29
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.69
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.42
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.67
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.00
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.62
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.02
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.95
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.93
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.04
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.93
 p-value of test no 153                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.67
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.33
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.67
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.45
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.92
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.26
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.74
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.56
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.30
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.36
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.00
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.97
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.98
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.75
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.73
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.77
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.48
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.99
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4698.63
 p-value of test no 173                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.10
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.31
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.51
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.62
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.40
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.55
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.93
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.28
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.12
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.58
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.69
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.52
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.07
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.11
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.42
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.97
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000117781
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.81
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000002266
 
 Normal statistic for number of bits   :   0.018
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:22.32
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193495065.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27945
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 32                 :    0.9985
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.84
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.60
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.53
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.15
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.44
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.14
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.59
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.38
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.94
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7256.68
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.95
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.12
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.98
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.66
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.20
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908229
   j =  2                              :            45869
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45391
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869391
   j =  1                              :        399909222
   j =  2                              :            45383
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.77
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.76
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.85
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.06
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.08
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.11
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.04
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.01
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17385.87
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.18
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.51
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.49
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.53
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.54
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.70
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.22
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.39
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.83
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.93
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.76
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.37
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.66
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.19
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.41
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.99
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.09
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.03
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.51
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.80
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.93
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4793.60
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.82
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.13
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.05
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.79
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.16
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.31
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.86
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.76
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.99
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.70
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.33
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.28
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.18
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.18
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.69
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.98
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.22
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.85
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.10
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.19
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.57
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999927230
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.07
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999920897
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:01.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194510873.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27946
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7557
 p-value of test no 19                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.39
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.35
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.08
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.17
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.06
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.62
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.26
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.09
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.53
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.14
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.69
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.46
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.80
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908226
   j =  2                              :            45881
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908102
   j =  2                              :            45946
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.83
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.38
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.79
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.78
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.57
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.51
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.66
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.65
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.04
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17202.85
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.69
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.96
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.17
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.79
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.89
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.82
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.22
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.11
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.72
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.99
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.95
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.59
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.42
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.78
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.22
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.66
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.11
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.98
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.04
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.74
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.77
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.98
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.88
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.45
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.85
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.44
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.70
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.94
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.09
 p-value of test no 176                :    0.9949
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.57
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.52
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.55
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.61
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.11
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.16
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.51
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.78
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.02
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.84
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.31
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.24
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.91
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.83
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000098218
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.81
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000140170
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    2.72
 p-value of test no 254                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:05.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195395609.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27947
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.38
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.72
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.92
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.24
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.70
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.41
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.26
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.91
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.95
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.97
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.19
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.62
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.61
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  160.28
 p-value of test no 67                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.79
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908201
   j =  2                              :            45895
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907962
   j =  2                              :            46013
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 116                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.82
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.83
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.61
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.22
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.91
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.40
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.00
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.23
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.05
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.91
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.31
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.64
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.61
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.76
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.15
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.92
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.15
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.77
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.58
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.67
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.58
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.61
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.20
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.37
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.41
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.90
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.02
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.27
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.75
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.94
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.88
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.48
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.98
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.02
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.25
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4757.75
 p-value of test no 173                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.68
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.69
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.56
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.02
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.43
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.96
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.58
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.15
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.59
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.15
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.50
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.99
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.19
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.58
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.33
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000056716
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.44
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000070969
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    2.31
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:15.28
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196640793.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27948
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 10                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7095
 p-value of test no 19                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    3.93
 p-value of test no 44                 :  9.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.33
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.47
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.64
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.31
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.64
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.92
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.80
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.23
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.07
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.88
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.17
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.71
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.93
 p-value of test no 66                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.36
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.49
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908100
   j =  2                              :            45947
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908443
   j =  2                              :            45771
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.97
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.06
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.55
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.45
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.95
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.98
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.37
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.09
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.68
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.04
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.52
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.44
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.78
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.92
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.56
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.37
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.06
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.49
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.14
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.30
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.71
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.20
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.31
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.95
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.64
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.58
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.50
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.03
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.55
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.46
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.86
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.64
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.49
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.64
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.87
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.42
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.39
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.26
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.11
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.73
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.43
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.65
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.58
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.67
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.55
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.14
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.63
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12272.38
 p-value of test no 229                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.07
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.76
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000009370
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.69
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999852179
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.066
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:14.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197885977.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27949
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9914
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.42
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.87
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.34
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.52
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.23
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.45
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.08
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.44
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6909.09
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.49
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.06
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.67
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.17
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.17
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908477
   j =  2                              :            45757
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908383
   j =  2                              :            45807
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.32
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.57
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.21
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   11.88
 p-value of test no 125                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.03
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.38
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17730.73
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.19
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.73
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.55
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.57
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.95
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.73
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.30
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.11
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.22
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.76
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.78
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.22
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.68
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.37
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.76
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.09
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.98
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.30
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.22
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.78
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.35
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.67
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.44
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.99
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.16
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.93
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.77
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.67
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.97
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.94
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.09
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.04
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.61
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.37
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.06
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.00
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.07
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.70
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.13
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.59
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000025303
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.14
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999982259
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.046
 p-value of test no 238                :    0.52
 
 Sample variance                       :    2.31
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:43.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199131161.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27950
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.70
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.34
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.66
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.56
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.82
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.07
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.68
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.13
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.26
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.56
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6880.59
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.44
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.21
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.57
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.69
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4749.19
 p-value of test no 68                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908728
   j =  2                              :            45630
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907891
   j =  2                              :            46053
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 86                 :  4.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    7.24
 p-value of test no 88                 :  2.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9998    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.81
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.69
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.96
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.91
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.50
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.88
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.74
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.28
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.93
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.53
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.17
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.00
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.21
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.51
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.17
 p-value of test no 150                :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.71
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.57
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.21
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.47
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.75
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.68
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.71
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.30
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.17
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.14
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.36
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.08
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.85
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.31
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.06
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.54
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.72
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4765.98
 p-value of test no 168                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.49
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.90
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.71
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.28
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.19
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.42
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.03
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.54
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.37
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.19
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.49
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.17
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.14
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.08
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4656.77
 p-value of test no 226                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.76
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.25
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.53
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.67
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.81
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999845894
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.94
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999853847
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 242                :    0.9990    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:42.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200114201.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27951
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5566
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 29                 :    0.9976
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    4.32
 p-value of test no 33                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.95
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.24
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.00
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.22
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.62
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.95
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.49
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.67
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.09
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.00
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 58                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.47
 p-value of test no 61                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.37
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.70
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.59
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45415
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869415
   j =  1                              :        399909172
   j =  2                              :            45411
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908170
   j =  2                              :            45903
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.68
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.74
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.52
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.37
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.30
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.12
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.35
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.08
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.71
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.08
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17220.06
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.93
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.84
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.95
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.12
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.33
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.67
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.61
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.47
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.65
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.11
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.23
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.12
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.88
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.48
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.07
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.94
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.32
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.34
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.09
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.46
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.91
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.40
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.97
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.97
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.47
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.30
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 180                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 182                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.43
 p-value of test no 183                :    0.9924
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.60
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.03
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.30
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.60
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.31
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.71
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.98
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.52
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.92
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.08
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.58
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.29
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000065902
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.72
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000024934
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 241                :    0.9916
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:44.22
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201031705.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27952
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5250
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.02
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.21
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.71
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.57
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.01
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.37
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.46
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.78
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6851.77
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.95
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.44
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.19
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.98
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908471
   j =  2                              :            45760
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907918
   j =  2                              :            46038
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 91                 :  8.7e-5    *****
 
 Anderson-Darling statistic = A2       :    8.68
 p-value of test no 92                 :  5.9e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.59
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.14
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.00
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.69
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.31
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.48
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.53
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.28
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.58
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.14
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.91
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.72
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.70
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.89
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.08
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.13
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.06
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.45
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.09
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.05
 p-value of test no 155                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.60
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.80
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.87
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.47
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.35
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.17
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.42
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.17
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.52
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.51
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.28
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.18
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.39
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.59
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.21
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.37
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.40
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.07
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.57
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.13
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.07
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 185                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.21
 p-value of test no 189                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.68
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.89
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.45
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9772.57
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.45
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.55
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.06
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.41
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.84
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.22
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.89
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000263581
 
 Normal statistic for number of bits   :    2.08
 p-value of test no 232                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.56
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000031258
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:58.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft AD, t = 24               5.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201916441.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27953
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 4                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 11                 :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.38
 p-value of test no 48                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.31
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.62
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.97
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.26
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.25
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.04
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.87
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.37
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.08
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.76
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908650
   j =  2                              :            45669
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907975
   j =  2                              :            46011
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 87                 :    0.9935
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 88                 :  7.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9980
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 105                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.43
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.67
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.56
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.14
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.22
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.85
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.34
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.99
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.02
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.40
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.97
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.27
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.73
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.13
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.89
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.64
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.71
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.05
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.73
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.18
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.18
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.04
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.23
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.25
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.33
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.34
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.22
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.58
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.94
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.87
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.24
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.14
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.18
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.18
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.42
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.28
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.62
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.14
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.09
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.91
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.85
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.46
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.70
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.81
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.38
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.85
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.96
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000054520
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.43
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999824447
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:56.40
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202932249.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27954
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1496
 p-value of test no 6                  :  2.3e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334616
   j =  1                              :        599997008
   j =  2                              :             1496
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    3.60
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.92
 p-value of test no 36                 :  9.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.81
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.93
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.49
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.93
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.75
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.23
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.30
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1526.69
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.12
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.58
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.66
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.01
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.90
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907848
   j =  2                              :            46070
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46049
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907904
   j =  2                              :            46045
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 93                 :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 95                 :  9.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9929
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.80
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.96
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.79
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.07
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.66
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.24
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.88
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.90
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.19
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17183.41
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.48
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.05
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.06
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.12
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.85
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.81
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.38
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.96
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.30
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.54
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.02
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.64
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.44
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.19
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.79
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.99
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.96
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.08
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5208.18
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.97
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.56
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.08
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.35
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.16
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.59
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.07
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.61
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.34
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.01
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.72
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.32
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.64
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.37
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.00
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.16
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.05
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.22
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.62
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999979085
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.38
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999926288
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:59.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   6  CollisionOver, t = 3            2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203980825.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27955
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 12                 :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5545
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9981
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.93
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.63
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.86
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.91
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.18
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.32
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.25
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.97
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.49
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.80
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.47
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.26
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.14
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908299
   j =  2                              :            45846
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908227
   j =  2                              :            45885
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.83
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.82
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.62
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.71
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.25
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.53
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 127                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    5.72
 p-value of test no 128                :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   71.37
 p-value of test no 129                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.18
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.99
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17784.51
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.38
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.01
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.46
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.98
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.15
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.42
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.47
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.59
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.87
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.51
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.12
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.55
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.76
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.54
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.63
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.45
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.55
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.97
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.86
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.31
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.40
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.01
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.61
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.65
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.03
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.38
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.82
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.17
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.19
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    2.03
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.16
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.30
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.07
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.60
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.25
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.46
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.05
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.28
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.24
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.05
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.53
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999919238
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.11
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000052513
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.058
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.037
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:27.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205029401.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27956
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.65
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.81
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.00
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.39
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.30
 p-value of test no 50                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.04
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.51
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.87
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1521.33
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.40
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.49
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.76
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.93
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.74
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.98
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908200
   j =  2                              :            45894
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908347
   j =  2                              :            45822
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 73                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 74                 :  2.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  2.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.30
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.34
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.76
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.10
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.73
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.91
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.85
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.25
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.46
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.37
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.08
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.39
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.72
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.93
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.77
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.34
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.87
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.16
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.08
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.59
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.07
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.96
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.75
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.10
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.14
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.23
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.37
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.56
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.49
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.14
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.25
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.58
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.05
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.75
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  471.06
 p-value of test no 172                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.47
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.37
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.73
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.09
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.38
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.53
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.19
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.85
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.09
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.25
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.41
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.25
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.39
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.93
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.36
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.14
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.21
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000179947
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.17
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999869333
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:34.02
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206110745.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27957
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    3.40
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    3.33
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.81
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.21
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.66
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.06
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.20
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.72
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.15
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.18
 p-value of test no 53                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.23
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.96
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.31
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.89
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.85
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.02
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.38
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.80
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.95
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907827
   j =  2                              :            46079
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45541
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869541
   j =  1                              :        399908919
   j =  2                              :            45539
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.03
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.71
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.86
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.60
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.96
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.03
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.24
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.26
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.02
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.53
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.03
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.20
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.51
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.46
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.45
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.41
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.90
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.16
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.72
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.71
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.66
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.58
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.22
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.22
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.31
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.50
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.46
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.44
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.00
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.77
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.98
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.27
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.77
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.41
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.12
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.91
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.77
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 185                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.88
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.09
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 205                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.23
 p-value of test no 207                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.42
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.86
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.74
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.15
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.16
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.31
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.44
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.10
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.46
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999869009
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.48
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999885149
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    2.17
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 241                :    0.9916
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:30.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206995481.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27958
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.46
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.15
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.97
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.22
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.76
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.38
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.39
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.80
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.04
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.62
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.43
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.62
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.42
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.52
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4852.55
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46174
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870174
   j =  1                              :        399907654
   j =  2                              :            46170
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908253
   j =  2                              :            45869
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.92e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-4
 p-value of test no 110                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.10
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.25
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.85
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.82
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.28
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.25
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.81
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.19
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.32
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.33
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 143                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17723.39
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.02
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.30
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.74
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.14
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.51
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.13
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.60
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.39
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.89
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.34
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.65
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.08
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.59
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.65
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.51
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.95
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.54
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.07
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.63
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.44
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.44
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.08
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.35
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.91
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.78
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.09
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.68
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.90
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.44
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.29
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.25
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.07
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.72
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.63
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.40
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.31
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.15
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.78
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.85
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000057358
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.10
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999962840
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:50.97
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208076825.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27959
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997179
   j =  2                              :             1409
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.80
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.34
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.47
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.64
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.08
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.82
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.02
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.74
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.79
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.60
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.12
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.74
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.00
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.76
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.09
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908179
   j =  2                              :            45906
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908580
   j =  2                              :            45707
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.30
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.23
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.22
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.20
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.19
 p-value of test no 124                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.56
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.60
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.36
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.83
 p-value of test no 136                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.53
 p-value of test no 137                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.78
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.23
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.01
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.94
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.27
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.08
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.49
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.74
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.68
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.13
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.00
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.35
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.57
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.01
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.42
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.46
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.28
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.75
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.70
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.53
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.22
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5178.16
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.14
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.79
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.95
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.23
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.33
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.48
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.41
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.11
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.97
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.86
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.75
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.39
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.25
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.04
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4344.26
 p-value of test no 227                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.74
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.46
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.26
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.56
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000099526
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.57
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000140773
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:57.52
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209125401.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27960
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.13
 p-value of test no 23                 :    0.9997    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.68
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.66
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.29
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.50
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.81
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.71
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.00
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.64
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.19
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.11
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.31
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.29
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 58                 :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.49
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.87
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.68
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.40
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45511
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869511
   j =  1                              :        399908982
   j =  2                              :            45503
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45459
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869459
   j =  1                              :        399909085
   j =  2                              :            45453
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.01
 p-value of test no 117                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.68
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.27
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.05
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.91
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.65
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.54
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.77
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17689.21
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.65
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.49
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.29
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.57
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.07
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.81
 p-value of test no 153                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.24
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.07
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.42
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.20
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.64
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.30
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.48
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.41
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.58
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.77
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.23
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.53
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.76
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.37
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.50
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.55
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.77
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.99
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.25
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.49
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.41
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.39
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.44
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.46
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.82
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.49
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.14
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.66
 p-value of test no 217                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.13
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.52
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3961.02
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.64
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.42
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.42
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.48
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999973031
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.87
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999956342
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:43.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189726746.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27961
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5274
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7125
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.64
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    3.53
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.43
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.25
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.23
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.31
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.46
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.40
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.23
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.52
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.36
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.62
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.62
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.58
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.25
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908267
   j =  2                              :            45862
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45356
 p-value of test no 71                 :    0.9928
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869356
   j =  1                              :        399909293
   j =  2                              :            45346
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 100                :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.10
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.00
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.09
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.03
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.65
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.66
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.08
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.13
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17200.11
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.96
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.50
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.60
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.67
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.91
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.37
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.51
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.27
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.28
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.24
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.03
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.13
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.67
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.78
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.78
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.22
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.60
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.31
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.94
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.25
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.74
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.54
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.60
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.14
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.80
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.45
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.18
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.54
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.32
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.52
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.44
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.37
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10235.21
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.96
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.43
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.72
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.02
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11550.46
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.23
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.89
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000031771
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.82
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999935264
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.20
 p-value of test no 249                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:12.39
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190545946.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27962
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    3.96
 p-value of test no 42                 :  9.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.79
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.14
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.02
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.71
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.31
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.76
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.59
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.09
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.69
 p-value of test no 58                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 60                 :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.20
 p-value of test no 61                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.62
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.60
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.25
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908632
   j =  2                              :            45681
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46087
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870087
   j =  1                              :        399907828
   j =  2                              :            46083
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 107                :    0.9942
 
 Anderson-Darling statistic = A2       :    5.05
 p-value of test no 108                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.40
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.55
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.92
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.48
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.31
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.33
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.90
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.05
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17267.31
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.07
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.84
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.42
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.72
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.24
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.50
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.37
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.22
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.46
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.41
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.72
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.87
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.81
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.82
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.36
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.56
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.36
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.76
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.80
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  301.89
 p-value of test no 169                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.05
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.88
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.71
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.26
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.83
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.62
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.37
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.64
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.00
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 209                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 210                :  7.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10386.13
 p-value of test no 211                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.67
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.10
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.66
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.80
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.64
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.75
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12119.12
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.97
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999869390
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.21
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000060562
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:08:35.96
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191266837.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27963
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.49
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.92
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.95
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.40
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.67
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.89
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.32
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.18
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.40
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6822.02
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.26
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.91
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.72
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5239.75
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907823
   j =  2                              :            46081
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907732
   j =  2                              :            46131
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 102                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.16
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.47
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.04
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.55
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.14
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.83
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.48
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.08
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17385.55
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.27
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.47
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.77
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.31
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.26
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.52
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.04
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.85
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.71
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.80
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.63
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.44
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.53
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.13
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.44
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.68
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.08
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.18
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.69
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.26
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5199.27
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.80
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.01
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.14
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.53
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.89
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.68
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.33
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.76
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.44
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.94
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.98
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.18
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.98
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.37
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.11
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.61
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.75
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.96
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11601.83
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.90
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999931760
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.14
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999903674
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:29.87
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192282645.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27964
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    2.97
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.23
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.51
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.80
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.17
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.09
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.01
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.68
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.27
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.65
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.62
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.09
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.77
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.80
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.11
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907736
   j =  2                              :            46129
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907772
   j =  2                              :            46108
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-6
 p-value of test no 112                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    5.31
 p-value of test no 114                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.13
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.16
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.85
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.02
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.24
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.22
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.90
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.90
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.76
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.96
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.81
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.85
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.93
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.29
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.00
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.34
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.26
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.20
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.16
 p-value of test no 158                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.09
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.71
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.90
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.36
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.03
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.96
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.57
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.73
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.92
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.42
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.23
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.85
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.06
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.97
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.32
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.79
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.51
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.14
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.30
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.53
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.09
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.63
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.54
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.83
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.70
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.88
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.62
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.66
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.17
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.29
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000091402
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.76
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000064708
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:14.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193560597.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27965
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.30
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.20
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.22
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.19
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.86
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.91
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.15
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.87
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.50
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.99
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.24
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.93
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908437
   j =  2                              :            45774
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.61
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.26
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.85
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.68
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.37
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.64
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.25
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.00
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.20
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.74
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.52
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.93
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.47
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.17
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.98
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.39
 p-value of test no 154                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.43
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.93
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.81
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.06
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.00
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.20
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.39
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.46
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.56
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.79
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.80
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.47
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.19
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.11
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.47
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.84
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.76
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.77
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.40
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.00
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.37
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.70
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.12
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.99
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.93
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.64
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.76
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.62
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.73
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.82
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999993740
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.52
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999919976
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:01.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194478101.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27966
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 10                 :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7551
 p-value of test no 15                 :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    3.11
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.47
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.64
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.27
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.48
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.01
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.73
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.20
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.80
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7268.56
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.72
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.20
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.13
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.65
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908175
   j =  2                              :            45908
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908591
   j =  2                              :            45697
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  4.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.22e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.55
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.50
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.97
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.04
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.31
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.49
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.82
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.14
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.87
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.86
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.46
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.02
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.62
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.33
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.93
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.37
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.08
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.30
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.56
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.53
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.35
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.91
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.66
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.42
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.28
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.85
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.58
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.95
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.99
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.13
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.58
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.20
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.36
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.77
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.91
 p-value of test no 172                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.27
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.60
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.36
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 185                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.06
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.26
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.22
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 208                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.71
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.52
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.03
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.43
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.31
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.46
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.06
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.97
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.50
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999983306
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.28
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999993425
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.057
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 248                :    0.9902
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:42.43
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195788821.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27967
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5294
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     541
 p-value of test no 31                 :    0.9923
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9980
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9925
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.30
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.08
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.37
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.94
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.88
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.35
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.81
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.70
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.31
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.64
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.70
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.29
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.75
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.27
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908285
   j =  2                              :            45850
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908174
   j =  2                              :            45910
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.93
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.11
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.55
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.27
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.54
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.74
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.87
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.60
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.11
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.59
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.95
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.05
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.31
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.56
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.18
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.83
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.30
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.79
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.77
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.59
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.39
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.69
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.28
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.84
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.09
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.29
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.72
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.09
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.56
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.85
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.51
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.61
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.54
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.28
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.13
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.56
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  446.55
 p-value of test no 174                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.87
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.11
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.96
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.88
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.35
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.01
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.22
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.45
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.29
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.73
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.41
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.46
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.83
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.41
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11561.52
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.70
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999888827
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.99
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000073210
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:11:04.23
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196804629.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27968
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5536
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.04
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.62
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.61
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.35
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.32
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.09
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.46
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.77
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.94
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.31
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.94
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.91
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5232.45
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907995
   j =  2                              :            45998
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908486
   j =  2                              :            45754
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 105                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.22e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.41
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.72
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.36
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.89
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.63
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.42
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.98
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.30
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.03
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.87
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.38
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.31
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.93
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.70
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.78
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.67
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.38
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.18
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.98
 p-value of test no 153                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.88
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.61
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.33
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.60
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.96
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.89
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.98
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.07
 p-value of test no 161                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.63
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.61
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.95
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.55
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.22
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.37
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.62
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.85
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.62
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.07
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.54
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.82
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.14
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.97
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9906
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.90
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.12
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.85
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.90
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.34
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.92
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.25
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.47
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.33
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.85
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12119.07
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.72
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999856418
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.76
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999990008
 
 Normal statistic for number of bits   :  -0.079
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.078
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:34.38
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197951509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27969
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.82
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.74
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.51
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.42
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.31
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.35
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.33
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1559.97
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.95
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.65
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.22
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.07
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.80
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46180
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870180
   j =  1                              :        399907646
   j =  2                              :            46168
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908340
   j =  2                              :            45827
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-4
 p-value of test no 112                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 114                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.31
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.07
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.55
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.33
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.77
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.10
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.28
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.92
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.79
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.61
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.43
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.67
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.70
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.42
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.90
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.05
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.63
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.39
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.01
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.80
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.51
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.15
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.60
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.83
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.61
 p-value of test no 161                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.91
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.71
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.84
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.19
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.05
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.04
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.98
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.17
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.08
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.89
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.01
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.06
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.23
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.84
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.81
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.49
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.61
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.50
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.03
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.89
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.02
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.99
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.11
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.92
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.30
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11540.95
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11536.00
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.61
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999966539
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.51
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999977942
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.35
 
 Sample variance                       :    2.23
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:07.79
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198967317.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27970
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.54
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.91
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.57
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.90
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.17
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.24
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.94
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.02
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.33
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.53
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.86
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.80
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.49
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.07
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.37
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908247
   j =  2                              :            45875
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907699
   j =  2                              :            46146
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.22
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.69
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.92
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.24
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.26
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.76
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.40
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.72
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.99
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.48
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.46
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.49
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.17
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.43
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.64
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.86
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.42
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.31
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.02
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.99
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.85
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.26
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.51
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.96
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.32
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.20
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.03
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.09
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.11
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.40
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.09
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.38
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.65
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.91
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.80
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.19
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.81
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.96
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.25
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.65
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-4
 p-value of test no 208                :    0.9990    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 210                :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10450.12
 p-value of test no 211                :  8.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10317.63
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4696.35
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.16
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4304.81
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.30
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.35
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.17
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.93
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999924557
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   27.88
 p-value of test no 233                :    0.9988
 
 
 -----------------------------------------------
 Total number of bits:  8000100969
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:19.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  90  HammingWeight2, r = 0           8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199983125.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27971
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7530
 p-value of test no 15                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.18
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.51
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.57
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.10
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.88
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.34
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.12
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.43
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.12
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.62
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.90
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.86
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.50
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46225
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870225
   j =  1                              :        399907550
   j =  2                              :            46225
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908134
   j =  2                              :            45924
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
 p-value of test no 90                 :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.23
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.88
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.36
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.67
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.15
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.75
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.10
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.24
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.21
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.74
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.61
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.45
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.34
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.40
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.50
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.09
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.39
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.32
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.17
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.36
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.80
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.72
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.60
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.97
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.07
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.22
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.60
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.72
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.51
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.54
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.06
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.84
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.83
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.38
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.70
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.63
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.43
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.97
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.54
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.84
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.88
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.01
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.98
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.36
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.93
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.81
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.16
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.59
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.37
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.82
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.07
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.03
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999977210
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.23
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000122140
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.82e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.06
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200900629.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27972
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5573
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.53
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.26
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.94
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.13
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.42
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.68
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.77
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.62
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.39
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.24
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.70
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.80
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.51
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.45
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908275
   j =  2                              :            45861
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908728
   j =  2                              :            45627
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.06
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.21
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.51
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.61
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.85
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.44
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.21
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.50
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.34
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.94
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.91
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.28
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.57
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.26
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.32
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.60
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.05
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.28
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.87
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.44
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.72
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.25
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.83
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.04
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.85
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.02
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.83
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.25
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.24
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.33
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.36
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.44
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.31
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.68
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.88
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  265.11
 p-value of test no 175                :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.07
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.95
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.92
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.44
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 210                :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.14
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.08
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.36
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.58
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.21
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.23
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.18
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.66
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.07
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999945818
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   92.95
 p-value of test no 233                :  7.8e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000071254
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:12.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201850901.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27973
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    4.15
 p-value of test no 24                 :  7.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    3.37
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.10
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.06
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.50
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.18
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.72
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.07
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.71
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.58
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.12
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7252.74
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.50
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.15
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.62
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.42
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908830
   j =  2                              :            45579
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907650
   j =  2                              :            46169
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.48
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.34
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.09
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.53
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.78
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.02
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.25
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.73
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.76
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.61
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.62
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.68
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.68
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.55
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.53
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.29
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.09
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.22
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.28
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.52
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.43
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.91
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.15
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.60
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.65
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.42
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.65
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.04
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.09
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.26
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.57
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.26
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.66
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.55
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.71
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.14
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.37
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.48
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.01
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.56
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.89
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5083.23
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.77
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.08
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.97
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.07
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.99
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999994628
 
 Normal statistic for number of bits   :  -0.042
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999903497
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:18.43
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203096085.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27974
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5237
 p-value of test no 13                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.68
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.99
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.27
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.63
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.66
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.47
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.89
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.52
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.75
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.77
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.25
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.01
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.72
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.96
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.43
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908267
   j =  2                              :            45859
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908052
   j =  2                              :            45971
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.48
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  104.74
 p-value of test no 120                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.76
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.71
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.54
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.43
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.26
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.57
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.41
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.27
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.71
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.48
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.70
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.68
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.98
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.07
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.31
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.44
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.83
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.60
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.40
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.70
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.99
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.18
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.05
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.73
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.09
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.86
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.22
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.71
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.89
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.70
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.76
 p-value of test no 172                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.65
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.93
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.66
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.35
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.72
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.98
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.36
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.99
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.37
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.67
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.49
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4325.38
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.05
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.26
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.00
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.36
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999904973
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.17
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999984437
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:01.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204242965.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27975
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    3.54
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.95
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.68
 p-value of test no 48                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.22
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.52
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.41
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  179.68
 p-value of test no 54                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.03
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.89
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7309.63
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.36
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 62                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.08
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.51
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.43
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.90
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907887
   j =  2                              :            46049
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45453
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869453
   j =  1                              :        399909098
   j =  2                              :            45445
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
 p-value of test no 94                 :    0.9981
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9906
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.63
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.82
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.71
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.96
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.62
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.32
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.52
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.35
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.96
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.30
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.12
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.36
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.84
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.00
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.60
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.84
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.60
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.45
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.63
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.08
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.77
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.09
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.52
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.53
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.23
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.33
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.67
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.88
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.71
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.34
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.57
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.55
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.44
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.92
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.12
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.00
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.88
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.64
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.54
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.31
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.80
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.32
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.51
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.35
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.06
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.65
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.21
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.28
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.38
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.24
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11431.47
 p-value of test no 230                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.74
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999885863
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.99
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999885377
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.085
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:43.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205291541.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27976
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 11                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7093
 p-value of test no 21                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.90
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.49
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.85
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.86
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.90
 p-value of test no 48                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.02
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.56
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.47
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.88
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.51
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.20
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.80
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.99
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.11
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.95
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.34
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.59
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907987
   j =  2                              :            46002
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908753
   j =  2                              :            45622
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  111.01
 p-value of test no 119                :  5.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.62
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.91
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.26
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.85
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.84
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.45
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 138                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.27
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17445.79
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.02
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.97
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.70
 p-value of test no 149                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.66
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.38
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.23
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.77
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.43
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.06
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.06
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.87
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.11
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.75
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.64
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.15
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.70
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.63
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.51
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.61
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.30
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.35
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.16
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.52
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.07
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.64
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.35
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.98
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.81
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.06
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.55
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.24
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.98
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.24
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.27
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.33
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.20
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.68
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.00
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.29
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.31
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.46
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999916838
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.88
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000009733
 
 Normal statistic for number of bits   :   0.077
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    2.16
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.077
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:28.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            5.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206405653.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27977
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5256
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4496
 p-value of test no 14                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.43
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.35
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.66
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.56
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.29
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.73
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.59
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.44
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.46
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.21
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7207.86
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.03
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.77
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.28
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.18
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.75
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45447
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869447
   j =  1                              :        399909109
   j =  2                              :            45441
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908249
   j =  2                              :            45868
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.42
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.48
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.39
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.41
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.67
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.81
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.29
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.74
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.63
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.46
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.17
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.74
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.89
 p-value of test no 152                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.31
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.67
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.64
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.82
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.33
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.18
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.35
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.73
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.15
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.99
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.44
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.79
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.36
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.99
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.00
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.60
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.73
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.25
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.98
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.26
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.34
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.74
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.30
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.91
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.85
 p-value of test no 203                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.76
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.27
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.12
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.20
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.09
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.13
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.36
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.17
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.06
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.13
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000043759
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.11
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999982883
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:32.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207421461.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27978
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9909
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.47
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.91
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.01
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.46
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.97
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.97
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.25
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.94
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.49
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.15
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.08
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.00
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5207.49
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908424
   j =  2                              :            45788
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908687
   j =  2                              :            45649
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.38
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.29
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.93
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.93
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.93
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.32
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.67
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.38
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.15
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.68
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.56
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.65
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.42
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.91
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.62
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.29
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.42
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.25
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.86
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.29
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.19
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.28
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.34
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.57
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.71
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.27
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.97
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.31
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.11
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.97
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.87
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.07
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.20
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.06
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.91
 p-value of test no 174                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.25
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 185                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    5.31
 p-value of test no 187                :  2.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.03
 p-value of test no 188                :    0.9988
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.87
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.94
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.92
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.18
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.99
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.64
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.10
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.88
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.11
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.73
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.72
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999879314
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.39
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000123640
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:19.69
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 208633877.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27979
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 38                 :    0.9950
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.65
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.92
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.34
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.08
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.75
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.11
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.00
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.12
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.11
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.85
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.51
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.97
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.06
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.25
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45618
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908768
   j =  2                              :            45610
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908207
   j =  2                              :            45886
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.86
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.29
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.95
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.57
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.01
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.95
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.67
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17417.68
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.31
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.19
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.12
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.39
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.18
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.10
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.22
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.01
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.64
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.28
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.37
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.89
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.35
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.08
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.50
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.03
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.27
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.43
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.28
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.00
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.22
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.74
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.22
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.15
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.66
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.26
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.06
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.80
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.52
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.47
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.64
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10312.17
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.38
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.28
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.95
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.16
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.95
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.54
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.57
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999875105
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.42
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000008389
 
 Normal statistic for number of bits   :   0.066
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.80e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:00:18.11
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 209747989.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27980
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7529
 p-value of test no 18                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.63
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.70
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.34
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.44
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.34
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.00
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.02
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.97
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.15
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.52
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.80
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.14
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.21
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908731
   j =  2                              :            45627
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.90
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.00
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.88
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.45
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.79
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.95
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.54
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.59
 p-value of test no 136                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.93
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.68
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.05
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.51
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.91
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.41
 p-value of test no 151                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.87
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.22
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.15
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.23
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.26
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.42
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.60
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.89
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.47
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.33
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.12
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.78
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.88
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.21
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.27
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.13
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.27
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.66
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.15
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.78
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.16
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 181                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.40
 p-value of test no 183                :    0.9917
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.57
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.98
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.40
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.69
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 209                :    0.9903
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9616.47
 p-value of test no 211                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.89
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.09
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.26
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.49
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.95
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.79
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.70
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.69
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999936749
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.51
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000052651
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:17:59.81
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 189759515.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27981
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.86
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.64
 p-value of test no 40                 :  4.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.84
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.06
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.53
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.55
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.71
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.00
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.59
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.22
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.34
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.50
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.12
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.92
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.16
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.20
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908787
   j =  2                              :            45605
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907912
   j =  2                              :            46038
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 104                :    0.9954
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.70
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.41
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.11
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.82
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.99
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.60
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.46
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.66
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.30
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.51
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17714.51
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.34
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.92
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.85
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.97
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.61
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.03
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.43
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.55
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.32
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.13
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.58
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.18
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.68
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.62
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.58
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.41
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.77
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.01
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.17
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.08
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.46
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.42
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.04
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.65
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.74
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.48
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.95
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.85
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.56
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.80
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.31
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.37
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.49
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 224                :    0.9934
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 225                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4615.36
 p-value of test no 226                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.09
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.90
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.94
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12070.01
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.00
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999991268
 
 Normal statistic for number of bits   :  -0.069
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.47
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000137812
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9948
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.063
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.79
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:19.64
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 190447643.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27982
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1229
 p-value of test no 10                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334349
   j =  1                              :        599997542
   j =  2                              :             1229
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    3.08
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.85
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9941
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.21
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.63
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.61
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.90
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.63
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.69
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.50
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.94
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.06
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.89
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.60
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.62
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.81
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.86
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908031
   j =  2                              :            45980
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908004
   j =  2                              :            45992
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.28
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.59
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.89
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.60
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.87
 p-value of test no 123                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.96
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.61
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.70
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.39
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.70
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.97
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.61
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.65
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.48
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.65
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.32
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.94
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.11
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.60
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.85
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.49
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.26
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.61
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.19
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.77
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.80
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.00
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.17
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.12
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.03
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.83
 p-value of test no 167                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.28
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.87
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.49
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.70
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.04
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.07
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.23
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.63
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.44
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.38
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.86
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.54
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.78
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.38
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.55
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.76
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.12
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.51
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.66
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.80
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999895379
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.76
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000046369
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:12:45.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 191561755.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27983
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.41
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.70
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.80
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.42
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.27
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.31
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.72
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.31
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.86
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.50
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.86
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.25
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.55
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.58
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.60
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907837
   j =  2                              :            46074
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908135
   j =  2                              :            45925
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.16
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.43
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.41
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.53
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.11
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.58
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.22
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.29
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.51
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.51
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.54
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.55
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.74
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.32
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.60
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.33
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.62
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.66
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.29
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.25
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.44
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.50
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.66
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.09
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.07
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.38
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.37
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.90
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.84
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.56
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.48
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.54
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.66
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.50
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.09
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.49
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.95
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.41
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.58
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.19
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.49
 p-value of test no 179                :  6.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-3
 p-value of test no 194                :    0.99
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.66
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.17
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.49
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.53
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.10
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.74
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.98
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.41
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.90
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11531.06
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.45
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.87
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999925511
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.18
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000074923
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:50.56
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 192741403.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27984
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 10                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.75
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.57
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.86
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.93
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.56
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.41
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.33
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.81
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.24
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.90
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.56
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.71
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908424
   j =  2                              :            45785
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908360
   j =  2                              :            45817
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.52
 p-value of test no 119                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.81
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.71
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.38
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.30
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.21
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.48
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.45
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.48
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.01
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.66
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.48
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.45
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.14
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.40
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.96
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.80
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.59
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.56
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.08
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.68
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.92
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.70
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.33
 p-value of test no 161                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.04
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.45
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.86
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  317.85
 p-value of test no 166                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.08
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.91
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.71
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.54
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.81
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.99
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.34
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.68
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.61
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.12
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.88
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.70
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.01
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.29
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.17
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.28
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.29
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.49
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.53
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.41
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.00
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.98
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.98
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.27
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999975149
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000015190
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 238                :    0.85
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:27.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 193691675.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27985
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9927
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.12
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.20
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.58
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.09
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.32
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.98
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.79
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  376.64
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.57
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.12
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.89
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
 p-value of test no 62                 :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 63                 :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.25
 p-value of test no 65                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.93
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.01
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908713
   j =  2                              :            45636
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908443
   j =  2                              :            45774
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
 p-value of test no 73                 :    0.9975
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-5
 p-value of test no 110                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.12
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.18
 p-value of test no 120                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.71
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.21
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.69
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.15
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.02
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.15
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.58
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17415.89
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.86
 p-value of test no 146                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.36
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.40
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.06
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.87
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.00
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.02
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.58
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.63
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.49
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.43
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.32
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.31
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.66
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.60
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.07
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.08
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.39
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.68
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.06
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.48
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.08
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.10
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.22
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.67
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.68
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.22
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.83
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.35
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.48
 p-value of test no 196                :    0.9930
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 201                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 202                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  257.23
 p-value of test no 203                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.46
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.70
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.12
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.26
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.84
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.18
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.96
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.86
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.28
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.12
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000001228
 
 Normal statistic for number of bits   : 9.71e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.01
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999827534
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.056
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:05:09.55
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 194576411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27986
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.61
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.24
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.47
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.27
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.71
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.12
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.08
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.49
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.52
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.68
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.32
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.51
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45561
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869561
   j =  1                              :        399908882
   j =  2                              :            45553
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45380
 p-value of test no 71                 :    0.9902
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869380
   j =  1                              :        399909243
   j =  2                              :            45374
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 84                 :    0.9970
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
 p-value of test no 100                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.56
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.71
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.87
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.57
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.45
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.45
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.15
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.97
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.49
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.85
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.17
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.58
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.98
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.93
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.33
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.72
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.47
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.40
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.96
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.66
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.66
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.02
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.56
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.66
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.62
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.37
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.89
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.50
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.58
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.08
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.67
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.78
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.62
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.79
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.06
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.29
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.05
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.07
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.70
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.98
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4723.40
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.50
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.09
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.85
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.82
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.61
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.80
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000160213
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.35
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000017053
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:52.45
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 195428379.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27987
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1254
 p-value of test no 7                  :    0.9987
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334374
   j =  1                              :        599997492
   j =  2                              :             1254
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.78
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.07
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.37
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.29
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.72
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.54
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.77
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.59
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7191.35
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.73
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.73
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.55
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.84
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.01
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908526
   j =  2                              :            45728
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45615
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908778
   j =  2                              :            45599
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
 p-value of test no 79                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 101                :  7.0e-4    *****
 
 Anderson-Darling statistic = A2       :    5.12
 p-value of test no 102                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.50
 p-value of test no 115                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.80
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.05
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.23
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.63
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.53
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.73
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.28
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.33
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.52
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.59
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.25
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.87
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.41
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.02
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.02
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.80
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.24
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.27
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.68
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.88
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.28
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.09
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.44
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.30
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.76
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.69
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.62
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.81
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.51
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.64
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.48
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.13
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.06
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.95
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.13
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.50
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.17
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.96
 p-value of test no 179                :    0.9984
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.87
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.95
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.55
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.42
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.09
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.17
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.80
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.19
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.12
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.31
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.64
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000092377
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.82
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000048226
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:18.29
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 196411419.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27988
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     837
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.97
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.27
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.90
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.28
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  290.36
 p-value of test no 54                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.17
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.15
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.39
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.97
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.69
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.22
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.86
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5204.24
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908075
   j =  2                              :            45961
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908004
   j =  2                              :            45989
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.58
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.28
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.54
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.29
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.43
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.74
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.78
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.50
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.74
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.62
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.76
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.03
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.80
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.69
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.54
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.15
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.17
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.45
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.34
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.56
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.77
 p-value of test no 163                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.11
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.80
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.70
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.90
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.69
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.23
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.13
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.22
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.66
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.98
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.26
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.96
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.76
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.51
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.21
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.92
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.51
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.04
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.65
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.07
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4698.30
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.25
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.96
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.52
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.95
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.96
 p-value of test no 231                :  4.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999960992
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.93
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000124342
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 235                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.55
 p-value of test no 238                :  5.4e-3
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:16.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 197361691.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27989
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9940
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 42                 :    0.9986
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.84
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.27
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.45
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.22
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.14
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.87
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.85
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.77
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.64
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.27
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.55
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.89
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.27
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5174.03
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908347
   j =  2                              :            45825
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908664
   j =  2                              :            45668
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
 p-value of test no 72                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.14
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.90
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.40
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.00
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.51
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.51
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.58
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.87
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.74
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.00
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.12
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.55
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.25
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.37
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.46
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   13.87
 p-value of test no 151                :    0.9997    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.22
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.28
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.38
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.23
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.20
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.13
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.45
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.25
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.92
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.59
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.05
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.19
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.38
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.71
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.57
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.28
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.60
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.14
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.59
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.38
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.57
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.95
 p-value of test no 174                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.91
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.90
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.19
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 181                :  2.7e-3
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    2.73
 p-value of test no 189                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.07
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.20
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.23
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.70
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.56
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.02
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.90
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.81
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.00
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.84
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.35
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.40
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999964442
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.27
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000041587
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-3
 p-value of test no 241                :    0.9983
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 243                :    0.9909
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:09:31.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 198410267.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27990
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.80
 p-value of test no 22                 :  3.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.67
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.39
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.24
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   89.14
 p-value of test no 50                 :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.13
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.58
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.04
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.08
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.27
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.91
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.18
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.92
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.30
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.55
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908150
   j =  2                              :            45922
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908674
   j =  2                              :            45657
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 86                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 108                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-5
 p-value of test no 113                :    0.9912
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.10
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.22
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.36
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.66
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.66
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.49
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.73
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-3
 p-value of test no 127                :    0.9987
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.46
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.62
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.28
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.41
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17385.45
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.09
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.49
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.86
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.80
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.45
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.76
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.76
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.42
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.21
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.08
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.01
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.73
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.52
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.93
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.46
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.66
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.92
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.47
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.37
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.05
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.35
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.94
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.02
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.58
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.54
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.60
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.42
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.44
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.95
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.40
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.52
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.09
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.78
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.73
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.29
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3927.29
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.38
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.73
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.91
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.77
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000083608
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.04
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000053059
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:06:18.37
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 199622683.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27991
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.60
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.14
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.64
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.12
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.07
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.95
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.40
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.54
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  511.56
 p-value of test no 55                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.61
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.31
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.64
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.65
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.35
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.25
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908583
   j =  2                              :            45701
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907911
   j =  2                              :            46040
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.19
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.66
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.81
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.46
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.76
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.35
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.63
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.27
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.86
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17338.93
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.39
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.79
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.51
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.18
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.30
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.39
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.74
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.47
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.75
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.56
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.41
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.65
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.37
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.91
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.39
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.30
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.04
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.46
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.23
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.09
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.67
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.06
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.74
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.13
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.82
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.74
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.37
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.44
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.50
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.70
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.69
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.55
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.49
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.52
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.90
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.89
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.17
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.51
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11553.23
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.35
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999962135
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.02
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999998903
 
 Normal statistic for number of bits   : -8.67e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:37.51
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 200704027.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27992
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.93
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.02
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.53
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.85
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.44
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.56
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.33
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.54
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.36
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.94
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.36
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.79
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.73
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908837
   j =  2                              :            45571
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907906
   j =  2                              :            46044
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.32
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.39
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.96
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.48
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.93
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.63
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.87
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17164.89
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.27
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.09
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.88
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.04
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.39
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.13
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.79
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.30
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.37
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.77
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.42
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.78
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.28
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.37
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.89
 p-value of test no 162                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.42
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.65
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.61
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.81
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.73
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.00
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.83
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.80
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.61
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.31
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.04
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.91
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.82
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.27
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.99
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.11
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.73
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.39
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.57
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.00
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.89
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.45
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.05
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.03
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.34
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.83
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999964607
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.93
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000071107
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:07:07.54
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 201687067.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27993
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.76
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.55
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.65
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.33
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.49
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.21
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.43
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.41
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.58
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.93
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.08
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.80
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.60
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.91
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.63
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908190
   j =  2                              :            45899
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907920
   j =  2                              :            46031
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-6
 p-value of test no 110                :    0.9978
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.86
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.28
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.76
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.45
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.75
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.98
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.72
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.54
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.65
 p-value of test no 134                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.34
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17229.09
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.34
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.22
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.75
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.45
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.54
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.42
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.52
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.42
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.62
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.18
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.53
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.22
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.25
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.49
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.63
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.99
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.30
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.40
 p-value of test no 166                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.90
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.35
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.91
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.46
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.71
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.42
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.78
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.55
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.36
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.77
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.48
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.80
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.17
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9873.77
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.17
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.13
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4313.43
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.41
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.41
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.00
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.42
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000043777
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.89
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000053749
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.83
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:10:07.95
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 202768411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27994
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    4.10
 p-value of test no 39                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.57
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.45
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.55
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.45
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  303.04
 p-value of test no 54                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.58
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.99
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.55
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.92
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.50
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.50
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.50
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908092
   j =  2                              :            45951
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908714
   j =  2                              :            45637
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.04
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.63
 p-value of test no 121                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.31
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.90
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.74
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.57
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.84
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 130                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.67
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.90
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17351.50
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.16
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.99
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.23
 p-value of test no 148                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.56
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.54
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.55
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.52
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.22
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.76
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.79
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.60
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.89
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.52
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.77
 p-value of test no 161                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.44
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.94
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.39
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.45
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.42
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.94
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.82
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.05
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.03
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.77
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.41
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.52
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.25
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.76
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.28
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.82
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.90
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.34
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.15
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.52
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.40
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.03
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.60
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.40
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.32
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.90
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.70
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.24
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000060139
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.47
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000016696
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    2.60
 p-value of test no 249                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:02:31.88
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 203948059.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27995
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9946
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.29
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.41
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.40
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.64
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.01
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.84
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.47
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.46
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.49
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.07
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.55
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.14
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.72
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5187.49
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908105
   j =  2                              :            45943
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908646
   j =  2                              :            45668
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.19
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.02
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.47
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.00
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.72
 p-value of test no 123                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.69
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.08
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.27
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17618.72
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.80
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.26
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.79
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.15
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.47
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.16
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.59
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.58
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.95
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.62
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.03
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.22
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.74
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.88
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.53
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.14
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.59
 p-value of test no 165                :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.43
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.60
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.74
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.82
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.23
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.70
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.07
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.72
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.18
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.65
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.06
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.12
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.08
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.72
 p-value of test no 203                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.09
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.89
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.84
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.05
 p-value of test no 217                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.47
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 223                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 225                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4641.31
 p-value of test no 226                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.36
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.14
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.22
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12168.35
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.59
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000012745
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.47
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000199663
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:53.04
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 204963867.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27996
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 10                 :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4479
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.05
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.08
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.84
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.16
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.71
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.90
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.74
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.69
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.50
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.64
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.08
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.94
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.73
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46018
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870018
   j =  1                              :        399907964
   j =  2                              :            46018
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908076
   j =  2                              :            45959
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
 p-value of test no 101                :    0.9976
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.70
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.76
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.78
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.10
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.24
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.97
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.03
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.85
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.053
 p-value of test no 134                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.17
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.47
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.59
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.78
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.25
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.89
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.36
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.70
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.76
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.75
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.46
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.35
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.72
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.84
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.77
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.29
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.87
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.26
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.20
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.24
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.82
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.43
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.68
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.53
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.73
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.44
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.20
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.26
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.16
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.67
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.18
 p-value of test no 196                :  4.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.30
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.72
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
 p-value of test no 209                :    0.9972
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9770.24
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.18
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.24
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.67
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.32
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.28
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.18
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.84
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.74
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000123349
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.65
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000143512
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:04:28.30
 
  All tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 205946907.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27997
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5272
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.14
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.27
 p-value of test no 49                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   96.53
 p-value of test no 50                 :  3.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.02
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.26
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.88
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.56
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.38
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7258.79
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.90
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.70
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.27
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.10
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.92
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908396
   j =  2                              :            45793
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46228
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870228
   j =  1                              :        399907547
   j =  2                              :            46222
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.88
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.16
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.33
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.15
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.83
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.32
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.88
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.68
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.34
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.47
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17102.19
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.17
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.79
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.69
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.82
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.08
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.99
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.03
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.03
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.29
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.74
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.50
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.01
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.01
 p-value of test no 161                :  2.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.79
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.62
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.37
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.02
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.31
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.45
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.85
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.26
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.68
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.77
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.14
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.09
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.34
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.11
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.78
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.72
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.89
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.47
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.09
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.82
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.91
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.10
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.16
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.01
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.75
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.87
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.20
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999855587
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.22
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999929783
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:30.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 206929947.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27998
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4548
 p-value of test no 16                 :  7.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.89
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    4.31
 p-value of test no 42                 :  6.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.61
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.53
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.39
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.87
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.54
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.84
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.23
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.31
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.07
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.41
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.96
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.02
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.86
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.68
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.75
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908551
   j =  2                              :            45720
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907824
   j =  2                              :            46082
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.61
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.14
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.22
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.72
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.35
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.64
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.52
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.24
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17474.95
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.06
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.50
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.28
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.46
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.29
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.98
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.46
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.02
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.67
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.00
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.81
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.65
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.53
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.44
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.85
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.87
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.82
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.28
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.10
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.88
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.75
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4714.86
 p-value of test no 168                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.99
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.65
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.08
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.48
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.33
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.31
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.50
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.81
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.80
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.13
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10295.51
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.22
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.35
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.72
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.38
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.97
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11533.75
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12177.39
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.50
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999797096
 
 Normal statistic for number of bits   :   -1.60
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.65
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000001735
 
 Normal statistic for number of bits   :   0.014
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    2.08
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:24.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 207945755.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 27999
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5552
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.19
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.53
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.85
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.12
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.70
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.39
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.44
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.75
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.63
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.71
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.92
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.61
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.77
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.88
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4854.44
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45593
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869593
   j =  1                              :        399908819
   j =  2                              :            45583
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908213
   j =  2                              :            45892
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 100                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.27
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.73
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.77
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.42
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.63
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.62
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.83
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.49
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.08
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.69
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.36
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.04
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.36
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.65
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.04
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.14
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.87
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.72
 p-value of test no 156                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.56
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.35
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.35
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.99
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.74
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.13
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.25
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.98
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.23
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.27
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.97
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.50
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.24
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.79
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.64
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.93
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.60
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.13
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.94
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.56
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.38
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.72
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.44
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.23
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.15
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10269.12
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.87
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.70
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.12
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.44
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.08
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11476.10
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.59
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999870281
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.55
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000101677
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 AHSrandom-TR 
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        AHSrandom-TR 
  Number of statistics:  160
  Total CPU time:   03:03:17.04
 
  All tests were passed
 
 
 
 
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